The Army has a long history of sending soldiers to compete in the Olympics. For instance, General George S. Patton first made his mark in the Army by representing America in the 1912 Olympics in the Modern Pentathlon. Not surprisingly, many of these athletes come from The Army Marksmanship Unit and compete in the shooting sports. More info can be found here.
The Army also has a World Class Athlete Program to recruit athletes who show a potential for Olympic competition.