Odom was born in South Jamaica, Queens, New York City, to Joe Odom and Cathy Mercer. His father was a heroin addict, and Odom's mother died of colon cancer when he was twelve years old. At her deathbed, Odom's mom told him: "Be nice to everybody". Afterwards, he was raised by his maternal grandmother, Mildred Mercer.

Odom contemplated entering the NBA directly out of high school, and consulted with Bryant, who had made the jump a year earlier. He decided he was not ready, and decided to attend the University of Nevada at Las Vegas. However, after a Sports Illustrated report questioned his unexpectedly high score of 22 out of 36 in the ACT, the school released him in July 1997 before he ever played a game for them. That same summer, he received a citation for soliciting prostitution following an undercover operation by the Las Vegas police. Later, an NCAA inquiry found Odom received payments amounting to $5,600 from booster David Chapman. Coach Bill Bayno was fired and UNLV was placed on probation for four years.  Odom transferred to the University of Rhode Island but was forced to sit out the 1997-98 season. He was admitted as a non-matriculating student, and was not allowed to play intramural basketball. His room and board was paid for by his father, who was covered by the G.I. Bill. After two semesters and a summer session, Odom earned his eligibility to play basketball. His career at Rhode Island had been in jeopardy after the first semester, when he vanished before finals. However, Rhode Island coach Jim Harrick persuaded three of his four instructors to allow him to make up his work. The coach also had Odom work with DeGregorio, who had become a Rams assistant and was the player's closest friend in college. Odom was also inspired by his maternal grandmother, a nurse who had raised five children and returned to school to earn her degree in 1980 at age 56.  Odom played one season for the Rams in the Atlantic 10 Conference, where he averaged 17.6 points per game and led the Rams to the conference championship in 1999. He earned first-team all-conference honors and was named the Atlantic 10 Rookie of the Year. He was named the most valuable player of the Atlantic 10 Tournament after his three-pointer against Temple University at the buzzer gave the Rams their first A-10 Tournament title.

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