To sportsmen with an eye for a challenge, an invitation to the Annual One-Shot Antelope Hunt in Lander, Wyo. can be as elusive a target as the speedy quarry itself. Each September a handful of politicians, entertainers and businessmen, chosen by a local committee, form up into three-man teams. Each squad's object: to kill one antelope per man, in the shortest time, without firing a single stray shot. Few participants have come to the hunt with more relish than Secretary of the Interior James Watt, 44, a Wyoming native, who viewed the event as a long-delayed rite of passage. "Since I was a boy," he said, "I always dreamed I'd be a big enough shot for the One-Shot."

Decked out in a red flannel shirt, a down jacket and a Day-Glo orange hunter's cap, Watt seemed delighted to be out of Washington. "It's good to be with real people," he said. Along with 17 other hunters, including Wyoming Gov. Ed Herschler, former Colorado Gov. John Love and three onetime Minnesota Vikings, he took part cheerfully in ersatz Shoshone Indian rituals designed especially for the occasion. One night he learned campfire dances from Wind River Reservation Indians, took on the nickname "Eeejjopo," meaning "Coyote" or "the Sly One," and became a Shoshone blood brother. The next evening he danced at the nearby Elks Club dressed as a squaw in black face paint and a purple shawl.

Not having hunted for 20 years, Watt seemed somewhat less at ease with a borrowed 25-06 rifle, designed for small game hunting. He missed a metal antelope 150 yards away during practice, then assured his team's defeat by loosing an errant shot at the flesh-and-blood version only 20 minutes into the hunt. One hour later, as consolation, the Secretary killed his first antelope ever. The species, according to a local fish and game commissioner, is overabundant, and its numbers must be reduced to prevent herd starvation. "Hunters take care of the land and manage wildlife so it will be here for subsequent generations," Watt declared. "They're the environmentalists that count."