Because of his lack of playing time at UCLA, few NBA teams had interest in Eaton after he finished his college career. He paid for two tryout camps, but only received an offer of $15,000 to play in Israel and another for $25,000 in Monte Carlo. However, the Utah Jazz, who finished in last place the prior season, saw him as a potentially dominant defender and selected him as a long-term project in the fourth round of the 1982 NBA draft with the 72nd overall pick. Utah coach Frank Layden quipped, "Like [former University of Utah coach] Jack Gardner said, 'You can't teach height'". Also the team's general manager, Layden discouraged him from playing in Europe and signed him to a five-year contract, with the first season guaranteed at $45,000, for a total $570,000.