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When convicted murderer Gary Gilmore was strapped to a chair in front of a firing squad on January 17, 1977, it had been a 10 years since a death sentence was carried out in America. Gilmore, a career criminal, was just three months out of prison when he robbed and shot to death two young men in Utah in July 1976. Both were students at Brigham Young University and both left widows with infants. That year, the U.S. Supreme Court ended a long moratorium on executions when it approved new state guidelines designed to make application of the death penalty constitutional. Gilmore's case attracted international attention when he refused to file an appeal, telling the judge, ''You sentenced me to die. Unless it's a joke or something, I want to go ahead and do it.'' Opponents of the death penalty fought to have his execution delayed, and he responded by twice attempting suicide and staging a 25-day hunger strike in protest of the unwanted legal efforts. Finally, after a flurry of 11th-hour legal activity, Gilmore was executed at Utah State Prison at 8 a.m. on January 17, 1977. His last words, before four bullets entered his chest, were ''Let's do it.'' Had he appealed his case, he likely would have lived another decade.