Private First Class Adame was a member of Company C, 1st Battalion, 1st Marines, 1st Marine Division. He was listed as Missing in Action while defending "Horseshoe Ridge", north of Chunchon and near the 38th Parallel against a Chinese assault on 23 April 1951. He was presumed dead on 17 December 1953. His name is inscribed on the Courts of the Missing at the Honolulu Memorial.

Adame was awarded the Purple Heart with Gold Star, the Combat Action Ribbon, the Korean Service Medal, the United Nations Service Medal, the National Defense Service Medal, the Korean Presidential Unit Citation and the Republic of Korea War Service Medal.