Vietnam Premier Pham Van Dong acknowledged Chinese sovereignty in writing
China's case against Vietnam is even stronger. It is not just the 1948 nine-dash line map and Article 15 of UNCLOS.
We also have a written document from Vietnam Premier Pham Van Dong conceding sovereignty over the South China Sea islands to China.
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Chinese South China Sea sovereignty is based on:
1.
China's historical first discovery and claim in 618 A.D.
South China Sea belongs to China because they discovered and claimed it.
Vietnamese and Filipinos should stop encroaching on thousand-year-old Chinese territory in the South China Sea.
[Source: Wikipedia article on Paracel Islands with primary sources listed in footnotes]
"The coast belonged to the Kingdom of Cauchi China."
"China
618~1279
* There are some Chinese cultural relics in the Paracel islands dating from the Tang and Song dynasty eras[12][note 1], and there is some evidence of Chinese habitation on the islands in these periods.[13]."
2.
Unchallenged Chinese dominion for over a thousand years.
The South China Sea islands and territory were claimed by the Tang, Song, and countless other Chinese dynasties. Vietnamese and Filipinos lacked ocean-faring boats and were not even aware of the existence of the Paracel and Spratly Islands from the 7th century to the 17th century.
3.
Historical written Chinese imperial records.
Tang, Song, and countless Chinese dynasties describe the Paracel and Spratly Islands as part of China.
4.
Physical proof of Chinese inhabitants
Our great-great-great-great-great-great-great-great-great-great-great-great-grandfather's bones and belongings are buried on the South China Sea islands. Our Chinese human remains and artifacts are similar to sacred Native American burial grounds of ancestors. The proof of dominion cannot be more clear.
The human remains of which country are found on South China Sea islands? China
The artifacts of which country are found on South China Sea islands? China
[Source: Wikipedia article on Paracel Islands with primary sources listed in footnotes]
5.
Vietnamese ceded any legal claim to the Paracel and Spratly Islands on September 14, 1958.
North Vietnam won the civil war against South Vietnam. Therefore, the diplomatic document signed by Vietnam Premier Pham Van Dong on September 14, 1958, which ceded Paracel and Spratly Islands to China, is in effect and legally binding.
Vietnam diplomatic document signed by Vietnam Premier Pham Van Dong
Translation of Vietnamese government's diplomatic document (shown above) into English:
The Democratic Republic of Vietnam's Government agree to terms of China's public statement on 9-4-1958 about China's sea territory claim. The Democratic Republic of Vietnam Government respect it, and will direct all Agencies to absolutely respect the 12 nautical miles sea territory of China in all matters with the People's Republic of China in the East Sea.
Sincerely,
Hanoi 14-9-1958.
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Translation of Vietnamese government's diplomatic document (shown above) into Mandarin/中文:
越南民主共和国承中华人民共和国在1958年9月4日关于中国领海主张的各项条款。越南民主共和国尊重,并且将要求所有越南部门尊重中华人民共和国在东海(我南海)12海里的领海的领海。
敬礼
河内,1958年9月14日
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"Declaration of the Government of the People's Republic of China on China's Territorial Sea (September 4,1958)" in Chinese as follows:
文中所提到的中华人民共和国在1958年9月4日关于中国领海主张的各项条款如下:
中华人民共和国政府宣布
  (一)中华人民共和国的领海宽度为12海里。这项规定适用于中华人民共和国的一切领土,包括中国大陆及 其沿海岛屿,和同大陆及其沿海岛屿隔有公海的台湾及其周围各岛、澎湖列岛、东沙群岛、西沙群岛、中沙群岛、 南沙群岛以及其他属于中国的岛屿。
  (二)中国大陆及其沿海岛屿的领海以连接大陆岸上和沿海岸外缘岛屿上各基点之间的各直线为基线,从基线 向外延伸12海里的水域是中国的领海。在基线以内的水域,包括渤海湾、琼州海峡在内、都是中国的内海、在基 线以内的岛屿,包括东引岛、高登岛、马祖列岛、白犬列岛、乌岳岛、大小金门岛、大担岛、二担岛、东碇岛在内 ,都是中国的内海。
  (三)一切外国飞机和军用船舶,未经中华人民共和国政府的许可,不得进入中国的领海和领海 上空。
  任何外国船舶在中国领海航行,必须遵守中华人民共和国政府的有关法令。
  (四)以上(一)(二)两项规定的原则同样适用于台湾及其周围各岛、澎湖列岛、东沙群岛、西沙群岛、南 沙群岛以及其他属于中国的岛屿。
  台湾和澎湖地区现在仍然被美国武力侵占,这是侵犯中华人民共和国领土完整的和主权的非法行为。台湾和澎 湖等地尚待收复,中华人民共和国政府有权采取一切适当的方法在适当的时候,收复这些地区,这是中国的内政, 不容外国干涉。
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Translation:
Declaration of the Government of the People's Republic of China on China's Territorial Sea (September 4,1958)
  The Government of the People's Republic of China declares:
  1. The breadth of the territorial sea of the People's Republic of China shall be twelve nautical miles. This provision applies to all territories of the People's Republic of China including the Chinese mainland and its coastal islands,as well as Taiwan and its surrounding islands,the Penghu Islands,the Dongsha Islands,the Xisha Islands,the Zhongsha Islands,the Nansha Islands and all other islands belonging to China which are separated from the mainland and its coastal islands by the high seas.
  2. China's territorial sea along the mainland and its coastal islands takes as its baseline the line composed of the straight lines connecting bas-points on the mainland coast and on the outermost coastal islands; the water area extending twelve nautical miles outward from this baseline is China's territorial sea. The water areas inside the baseline,including Bohai Bayand the Chiung chow Straits,are Chinese inland waters. The islands inside the base line,including Tungyin Island, Kaoteng Island,the Matsu Islands,the Paichuan Islands,Wuchiu Island,the Grater And Lesser Quemoy Islands,Tatan Island,Erhtan Island and Tungting Island,are islands of the Chinese inland waters.
  3. No foreign aircraft and no foreign vessels for military use may enter China's territorial sea and the air space above it without the permission of the Government of the People's Republic of China.
  While navigation Chinese territorial sea,every foreign vessel must observe the relevant laws of the People's Republic of China and regulations of its government.
  4. The principles provided in paragraphs (2) and (3) apply also to Taiwan and its surrounding islands,the Penghu Islands,the Dongsha Islands,the Xisha Islands,the Zhongsha Islands,the Nansha islands, and all other islands belonging to China.
  The Taiwan and Penghu areas are still occupied by the United States armed force. This is anunlawful encroachment on the territorial integrity and sovereignty of the People's Republic of China. Taiwan,Penghu and such other areas are yet to be recovered,and the Government of the People's Republic of China has the right to recover these area by all suitable means at a suitable time. This is China's internal affair,in which no foreign interference is tolerated.
[Note: Thank you to FrankLau for the post and translation.]
6.
The entire Vietnamese government admitted to Chinese sovereignty over the South China Sea islands and territory.
On June 15, 1956, Vice Foreign Minister of the DRV (North Vietnam) Ung Van Khiem admitted Chinese sovereignty over the Spratly and Paracel Islands.
Another DRV official, Le Loc (Temporary Head of the Asian Mission), concurred in Chinese sovereignty over South China Sea islands.
In their civil war, North Vietnam (i.e. Democratic Republic of Vietnam or DRV) conquered South Vietnam and became the government of an unified Vietnam. Let's hear it directly from the DRV's mouth with regards to Chinese sovereignty over the Paracel Islands.
"Truong Nhan Tuan:
Based on a number of documents from Peking, on 15/6/1956 the Vice Foreign Minister of the DRV Ung Van Khiem, at the time of hosting a visit from the Chinese temporary ambassador in Vietnam, spoke the following: “According to documents that Vietnam has presently, historically speaking, Tay Sa and Nam Sa islands belong to China.”
Nguyen An:
Tay Sa and Nam Sa means the Paracel and Spratly islands?
Truong Nhan Tuan:
Yes, the Paracel and Spratly islands....China also presents other evidence, such as the incident of Le Loc (Temporary Head of the Asian Mission) also present at that time adding that: “From a historical perspective, the archipelagos of Xi Sa and Nan Sa (Tay Sa and Nam Sa) belonged to China since the T’ang dynasty.
Nguyen An:
Le Loc is a person of China or of the DRV?
Truong Nhan Tuan:
An official of the DRV."
...
"Nguyen An: Are there other evidence from the DRV presented by China regarding sovereignty?
Truong Nhan Tuan: Yes. The famous one is the diplomatic note of Pham Van Dong, written on 14/9/1958 which admits the territorial waters declared by China a few days before. The Chinese declaration was that the archipelagos of Hoang Sa, Nam Sa, and Truong Sa belonged to China.
Nguyen An: So it was an admittance of Chinese sovereignty over these islands?
Truong Nhan Tuan: In reality, there is nothing in the content of the letter that explicitly states admittance of Chinese sovereignty over the Paracel and Spratly islands becaue the letter only states that Vietnam “make notes and admits the declaration of China regarding territorial waters of China” but does not mention about sovereignty over the Paracel and Spratly archipelagos.
What makes the justification somewhat weak is because during the war, when the Chinese navy invaded the Paracel islands in 1974, there was no objection from the DRV. This silence becomes a weighty piece of evidence for China to claim that Vietnam had admmitted Chinese sovereignty over the Paracel and Spratly archipelagos already.
Nguyen An: Based on what you just presented, is this the reason why Qin Gang (Chinese Foreign Ministry Spokesperson) commented that Vietnam’s position regarding sovereignty over the Paracel and Spratly archipelagos changed over different periods of time?
Truong Nhan Tuan: This is correct. But the legal significance is not simple. Declarations made by officials in North Vietnam at that time may be a reality. The fact that Peking presents them without protestations or justifications from Hanoi tells us that it is probably true."
Reference: [Source: Vietnamese historian's research into Paracel Islands]