In 1978 Kiraly enrolled at UCLA, where he majored in biochemistry and also was a brother of the Epsilon Sigma Chapter of Lambda Chi Alpha. From his freshman year, he played outside hitter and setter on the Bruins' volleyball team, playing opposite junior Sinjin Smith in the Bruins' 6–2 offense. Under head coach Al Scates, Kiraly led UCLA to the NCAA Men's Volleyball Championship in his freshman season in 1979. In his sophomore season, the Bruins made it to the finals again, but lost to crosstown rivals USC. UCLA reclaimed the top spot in Kiraly's junior season. Kiraly finished his college career with another title during his senior year. In his four years, the Bruins compiled a 123–5 match record, with titles in 1979, 1981 and 1982. They went undefeated in the 1979 and 1982 seasons. Kiraly earned All-American honors all four years, and was awarded NCAA Volleyball Tournament Most Outstanding Player in 1981 and 1982.