Vietnam is a nation in Southeast Asia. In actual history, the U.S. withdrew its forces at the end of a prolonged conflict and its ally South Vietnam fell to the Communist forces of North Vietnam in 1975. In the Watchmen universe, President Richard M. Nixon's dispatch of Dr. Manhattan to Vietnam ensures a U.S. victory by 1971, and Vietnam later becomes the 51st state.
The Comedian fought for the U.S. in Vietnam. On the night of the declaration of the United States victory in the war, he drunkenly shoots and kills a young Vietnamese woman whom he has impregnated when she attacks him with a bottle, cutting his face. He notes that Dr. Manhattan could easily have prevented his crime.
In October 1985 the New York Times had the headline "Vietnam 51st State: Official!". A graffiti saying "Viet Bronx" is found outside Happy Harry's Grill, apparently written by a gang that identifies or sympathizes with the Vietnamese people.