Vietnam is a nation in Southeast Asia. In actual history, the United States withdrew its forces in 1975 at the end of a prolonged conflict. Subsequently it's ally, South Vietnam, fell to the Communist forces of North Vietnam. In the Watchmen universe, President Richard M. Nixon's dispatch of Dr. Manhattan to Vietnam ensures a U.S. victory by 1971. The Comedian fought for the U.S. in Vietnam.
On the night of the declaration of the United States victory in the war, Nixon arrives on a helicopter. The Comedian 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.