On October 11, 1993, 18-year-old Julie Heath was driving on U.S. Highway 270 between Malvern and Hot Springs, Arkansas to visit her boyfriend in Hot Springs. Nance stated that he stopped to help Heath after her car broke down and offered her a ride to Malvern. The prosecution said that Nance then raped and murdered her. He was later seen in a convenience store wearing no shoes, socks, or shirt. According to the clerk, there appeared to be fresh dark, damp stains on his overalls.  Heath’s body was found on October 18, 1993 by a hunter. Her throat had been cut. Photographs of the scene show that she was fully clothed, but her belt buckle was partially undone, her pants zipper was not fully up, and the left shoulder of her shirt was torn. The shirt was also on inside out. The medical examiner also reported that her socks and panties were on inside out and her bra was pulled up around the neck and shoulder area. A pubic hair located in Nance’s pickup was said by an expert to be microscopically identical to that of Heath.  Nance said he accidentally killed Heath. According to defense testimony, she had become hysterical after seeing a utility knife and began to kick at him. Putting up his hand to stop her, he accidentally lodged the knife in her throat. This version of events were told at the trial by his brother and sister, to whom Nance had told his version of events.

Nance was found guilty of capital felony murder, with attempted rape as the underlying felony. During the sentencing phase of the trial, it was revealed that five months before the murder, Nance had been released from a twenty-year sentence for beating two Oklahoma girls in 1982. The jury found that there were no mitigating circumstances in the case, and recommended that the judge sentence Nance to death, which he did on March 31, 1994.  His lawyers argued that it would be unconstitutional (Atkins v. Virginia) to execute Nance, as he was mentally retarded. A psychologist said that Nance had an IQ below 70, whereas a psychiatrist testified that he found Nance to have an IQ of 105. The defense also argued that DNA tests could show that the pubic hair did not come from Heath.  On November 17, 2005, the Arkansas Parole Board recommended, with a vote of 6-1, that Governor Mike Huckabee deny clemency for Nance. The dissenting vote was from one member who wanted to stay the execution to give more time to determine if Nance was mentally retarded.  The execution was briefly stayed on November 17 by United States federal judge James Moody of the Eastern District of Arkansas. The stay was vacated by the 8th Circuit Court of Appeals on November 19.