Rice was born in Salisbury, North Carolina, to Allison Rice and Wayne Jefferson. His parents ended their relationship soon afterward. Rice attended L. C. Bird High School in Chesterfield, Virginia, and played on the school's basketball team. In his junior and senior seasons, he earned AAA All-State honors from the Virginia High School Coaches Association. In the 2004–05 season, he led his team to a school-record 29 wins and a Central Region title, their first ever. Rice averaged 27.0 points, 6.2 assists and 5.0 rebounds per game that season. He earned 2004–05 Associated Press (Virginia) Co-Player of the Year honors and was named (Richmond) Times-Dispatch Player of the Year.
Rice signed his letter of intent to play basketball at and attend Boston College on April 28, 2005. As a freshman (2005–06), Rice played in all 36 games, averaging 9.3 points, 1.4 rebounds and 2.5 assists per game. He earned two ACC rookie honors: ACC Rookie of the Week on November 28, 2005 and was named to the ACC All-Freshman team. In his sophomore season (2006–07), Rice started all 33 games, averaging 36.6 minutes a game. He finished the season with stats of 17.6 points, 3.4 rebounds and 5.4 assists per game. Rice was named to the All-ACC second team, and garnered All-Tournament honors for that season's ACC tournament. In two NCAA tournament games, Rice averaged 24 points. A highlight of Rice's junior season (2007–08) was a career-high 46-point performance in a 90–80 home loss to North Carolina on March 1, 2008. He scored 34 points by halftime. Rice averaged 21.0 points, 3.3 rebounds and 5.0 assists per game. He again earned All-ACC honors, this time on the first team. In a scintillating senior year (2008–09), Rice experienced a dip in his scoring, averaging 16.9 points a game but improved in other statistical categories, averaging 3.8 rebounds and 5.4 assists a game. He scored 9 points in BC's only appearance of the 2009 NCAA tournament.
On July 11, 2013, Rice signed a two-year contract with Israeli champions Maccabi Tel Aviv. In his first season with Maccabi, he won the Euroleague, with him averaging 9.5 points, 3.2 assists and 2.1 rebounds over 30 games. After beating favored Olimpia Milano in dramatic playoff series, Maccabi advanced to the Euroleague Final Four. In the semifinal game, he was responsible for the 68–67 victory over CSKA Moscow by scoring the game-winner with 5.5 seconds left on the clock. In the championship final game against Real Madrid, he scored 26 points, leading his team to a sixth Euroleague title, after ovetime 98-86 victory. For such performance, he was named the Final Four MVP of the Euroleague.
On June 30, 2014, Rice signed a three-year deal with the Russian club Khimki.