Question: Which war occurs first, Battle of Peleliu or the Battle of the Ch'ongch'on River?

Context paragraphs:
Eighth Army Ranger Company: The Eighth Army Ranger Company, also known as the 8213th Army Unit, was a Ranger light infantry company of the United States Army that was active during the Korean War.  As a small special forces unit, it specialized in irregular warfare.  Intended to combat the North Korean (NK) commandos who had been effective at infiltration and disruption behind United Nations (UN) lines, the Eighth Army Ranger Company was formed at the height of the Battle of Pusan Perimeter in September 1950 and was the first U.S. Army Ranger unit created since World War II.  The company went into action as a part of the 25th Infantry Division during the UN advance into North Korea in October and November.  It was best known for its defense of Hill 205 against an overwhelming Chinese attack during the Battle of the Ch'ongch'on River which resulted 41 of the 51 Rangers becoming casualties.

USS Peleliu: USS "Peleliu" (LHA-5) was a "Tarawa"-class amphibious assault ship of the United States Navy, named for the Battle of Peleliu of World War II.  Entering service in 1980, she has been deployed to the Persian Gulf on several occasions, performed an evacuation of U.S. Naval Base Subic Bay following the eruption of Mount Pinatubo, operated with the INTERFET peacekeeping taskforce, participated in Pacific Partnership deployments, and provided assistance following the massive floods in Pakistan in 2010.  She was decommissioned in San Diego, California on March 31, 2015.  She currently rests, out of commission and in reserve, at NAVSEA Inactive Ships On-site Maintenance Office, Pearl Harbor, Hawaii alongside USS "Tarawa" in the inactive reserve in case of further need.

Kloulklubed: Kloulklubed is the main settlement on the Palau island of Peleliu.  it is situated at the northern end of the island, close to North beach.  The village was a centre of Japanese operations during World War II, and the remains of the Japanese communications centre is still standing in the village.  A monument to the Battle of Peleliu is also located in the village.

Battle of Peleliu: The Battle of Peleliu, codenamed Operation Stalemate II by the United States military, was fought between the U.S. and the Empire of Japan during the Mariana & Palau Campaign of World War II, from September to November 1944, on the island of Peleliu.

Herbert J. Ray: Rear Admiral Herbert James Ray (1 February 1893 – 3 December 1970) was an officer in the United States Navy who served in World War I and World War II.  A 1914 graduate of the Naval Academy, he served on the submarines USS "H-2" and "N-3" during World War I.  In March 1942, as Chief of Staff and Aide to the Commandant of the Sixteenth Naval District, Rear Admiral Francis W. Rockwell, he participated in General Douglas MacArthur's escape from the Philippines.  In Australia, he served with MacArthur's General Headquarters, Southwest Pacific Area staff.  In September 1943, he became Captain of the battleship USS "Maryland" , which he commanded in the Battle of Tarawa, Battle of Kwajalein, Battle of Saipan and the Battle of Peleliu.  In October 1944, he participated in the Battle of Surigao Strait, in which "Maryland" joined the other battleships in engaging the Japanese battleships "Fusō" and "Yamashiro" and their escorts.  Ray left "Maryland" in December 1944, and was appointed Deputy Director of the Naval Division of the US Control Group Council for Germany.  After VE Day, he became the Junior United States Member of the Tripartite Naval Commission in Berlin.  He retired from the Navy on 30 June 1949, and received a tombstone promotion to rear admiral due to his combat decorations.

USS Honolulu (CL-48): USS "Honolulu" (CL-48) of the United States Navy was a "Brooklyn"-class light cruiser active in the Pacific War (World War II).  "Honolulu" was launched in 1937 and commissioned in 1938.  The ship served in the Battle of Tassafaronga, the Battle of Kula Gulf, the Battle of Kolombangara and the Battle of Peleliu.  She was taken out of action by serious torpedo damage just before the Battle of Leyte Gulf.  She was repaired, but did not return to the Pacific war.  She was decommissioned in 1947 and was held in reserve until she was scrapped in 1959.

Third Battle of Seoul: The Third Battle of Seoul, also known as the Chinese New Year's Offensive, the January–Fourth Retreat (Korean: 1•4 후퇴 ) or the Third Phase Campaign Western Sector (), was a battle of the Korean War, which took place from December 31, 1950 to January 7, 1951 around the South Korean capital of Seoul.  In the aftermath of the major Chinese victory at the Battle of the Ch'ongch'on River, the United Nations Command started to contemplate the possibility of evacuation from the Korean Peninsula.  Upon learning of this development, China's Chairman Mao Zedong ordered the Chinese People's Volunteer Army to cross the 38th parallel in an effort to pressure the United Nations forces to withdraw from South Korea.

Peleliu: Peleliu (or Beliliou) is an island in the island nation of Palau.  Peleliu forms, along with two small islands to its northeast, one of the sixteen states of Palau.  The island is noted as the location of the Battle of Peleliu in World War II.

Battle of the Ch'ongch'on River: The Battle of the Ch'ongch'on River, also known as the Battle of the Ch'ongch'on () or the Second Phase Campaign Western Sector (), was a decisive battle in the Korean War, and it took place from November 25 to December 2, 1950, along the Ch'ongch'on River Valley in the northwestern part of North Korea.  In response to the successful Chinese First Phase Campaign against the United Nations forces, General Douglas MacArthur launched the Home-by-Christmas Offensive to evict the Chinese forces from Korea and to end the war.  Anticipating this reaction, the Chinese People's Volunteer Army Commander Peng Dehuai planned a counteroffensive, dubbed the "Second Phase Campaign", against the advancing UN forces.

Battle of Wawon: The Battle of Wawon (Turkish: "Kunuri Muharebeleri" ), also known as the Battle of Wayuan (), was a series of delay actions of the Korean War that took place from November 27–29, 1950 near Wawon in present-day North Korea.  After the collapse of the US Eighth Army's right flank during the Battle of the Ch'ongch'on River, the Chinese 38th Corps advanced rapidly towards the critical road junction at Kunu-ri in an effort to cut off United Nations forces' retreat route.  In what was considered to be Turkey's first real combat action since the aftermath of World War I, the Turkish Brigade attempted to delay the Chinese advances at Wawon.  Although during the battle the Turkish Brigade was crippled after being encircled by Chinese forces with superior numbers, they were still be able to breach the Chinese trap and rejoin the US 2nd Infantry Division.

Supporting paragraphs: Battle of Peleliu Battle of the Ch'ongch'on River
Answer: Battle of Peleliu