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 by changing the physical matter involved (the Comedian's pistol) or that he could have teleported either of them out of danger.
In October 1985 the New York Times had the headline "Vietnam 51st State: Official!". A piece of graffiti saying "Viet Bronx" is found outside Happy Harry's Grill, apparently written by a gang that identifies or sympathizes with the Vietnamese people.