Question: William Frederick Harris received the Navy Cross for extraordinary heroism during the breakout in a battle that took place in which war ?

Context paragraphs:
Battle of Chosin Reservoir: The Battle of Chosin Reservoir, also known as the Chosin Reservoir Campaign or the Changjin Lake Campaign (Korean: 장진호 전투 ; hanja: 長津湖戰鬪; rr: "Jangjin ho jeontu"; ), was a decisive battle in the Korean War.  The name "Chosin" is derived from the Japanese pronunciation ""Chōshin"", instead of Korean pronunciation

William Frederick Harris: William Frederick Harris (6 March 1918 – 7 December 1950) was a United States Marine Corps Lieutenant Colonel during the Korean War.  He was the son of USMC General Field Harris, a Prisoner of War during World War II and a recipient of the Navy Cross for extraordinary heroism during the breakout in the Battle of Chosin Reservoir.  He was last seen by American forces on 7 December 1950, was listed missing in action and is presumed to have been killed in action.  Harris was featured in the and film "Unbroken".

Navy Cross: The Navy Cross is the United States military's second-highest decoration awarded for valor in combat.  The Navy Cross is awarded primarily to a member of the United States Navy, U.S. Marine Corps, and the U.S. Coast Guard (when operating under the Department of the Navy) for extraordinary heroism.  The medal is equivalent to the Army Distinguished Service Cross, the Air Force Cross, and the Coast Guard Cross.

Intelligence Star: The Intelligence Star is an award given by the Central Intelligence Agency to its officers for "voluntary acts of courage performed under hazardous conditions or for outstanding achievements or services rendered with distinction under conditions of grave risk".  The award citation is from the Director of the Central Intelligence Agency and specifically cites actions of "extraordinary heroism".  It is the third-highest award given by the Central Intelligence Agency, behind the Distinguished Intelligence Cross and Distinguished Intelligence Medal, and is analogous to the Silver Star, the US military award for extraordinary heroism in combat.  Only a few dozen people have received this award (most posthumously), making it one of the rarest valor awards awarded by the US government.

John Basilone: John Basilone (November 4, 1916 – February 19, 1945) was a United States Marine Corps gunnery sergeant who was killed in action during World War II.  He received the Medal of Honor for heroism above and beyond the call of duty during the Battle for Henderson Field in the Guadalcanal Campaign, and the Navy Cross posthumously for extraordinary heroism during the Battle of Iwo Jima.  He was the only enlisted Marine to receive both of these decorations in World War II.

John McNulty (U.S. Marine Corps): Maj. John McNulty of Revere, Massachusetts (fl.  c. 1918), American Expeditionary Forces, was a U.S. Marine Corps’ World War I war hero.  For his service in that conflict, then, 1st Sgt. McNulty was awarded the Navy Cross (for “Extraordinary heroism in combat not justifying the Medal of Honor”), the Distinguished Service Cross (United States) (for “Distinguishes himself by extraordinary heroism not justifying the Medal of Honor”) and, twice, the Silver Star (for “gallantry in action against an enemy of the United States”).

George Cregan: George Cregan (December 11, 1885 – June 30, 1969) was a commander in the United States Navy.  He was a recipient of the Medal of Honor, the nation's highest military award for valor, for his role in the United States occupation of Veracruz when he was a coxswain.  He was also awarded the Navy Cross, the second highest military decoration awarded to a member of the United States Navy, U.S. Marine Corps and to members of the Coast Guard for extraordinary heroism.  He received the Navy Cross for his participation in the 1929 salvage operation of the submarine USS S-4.

John Bradley (United States Navy): John Henry "Jack" "Doc" Bradley (July 10, 1923 – January 11, 1994) was a United States Navy Hospital corpsman who was awarded the Navy Cross for extraordinary heroism in combat on February 21, 1945 while assigned to a U.S. Marine Corps rifle company during the Battle of Iwo Jima in World War II.

Coast Guard Cross: The Coast Guard Cross is a military decoration of the United States Coast Guard.  Established by Act of Congress on 15 October 2010, it is intended to recognize members of the United States Coast Guard for extraordinary heroism in action, while not operating under the Department of the Navy.  Coast Guard members serving under the United States Navy would be eligible for the Navy Cross.  This medal, though approved, has not yet been awarded.

USS Lloyd Thomas (DD-764): The third USS "Lloyd Thomas" (DD/DDE-764) was a "Gearing"-class destroyer in the United States Navy during the Korean War and the Vietnam War.  She was named for Lieutenant (j.g.) Lloyd Thomas (1912–1942), who was posthumously awarded the Navy Cross for extraordinary heroism in the Battle of Midway.

Supporting paragraphs: William Frederick Harris Battle of Chosin Reservoir
Answer: the Korean War