May grew up in Bloomington, Indiana. He was a three-time all-state selection at Bloomington North High School, and was at one time a teammate of current NBA player Jared Jeffries. When the heavily-recruited May chose to attend the University of North Carolina at Chapel Hill, it was a major surprise to most basketball recruiting observers; it had been thought that he would stay in his hometown and attend Indiana. He had strong family connections to IU; his father Scott was a forward on the school's undefeated national championship team in 1976 and won the Naismith Award the same year, and his brother Scott Jr. played for the IU team that made the NCAA title game in 2002.
At North Carolina, May made his mark as the starting center for the Tar Heels basketball team from 2003 to 2005. As a junior, May was named MVP of the 2005 NCAA tournament after leading North Carolina to its 5th national championship when they beat the University of Illinois by a score of 75-70.
In April 2005, May declared that he would forego his senior year at UNC to enter the NBA Draft. He was selected 13th overall by the Charlotte Bobcats, becoming one of four Tar Heels to be lottery picks in the 2005 NBA Draft.