Duberry attended Enfield Grammar School in London and started his career at Chelsea where he was a trainee and made his debut during the 1993–94 season, before a brief loan period with AFC Bournemouth. Duberry made a total of 115 appearances for Chelsea and scored 3 goals, including one in a 2–1 win over Manchester United at Old Trafford in November 1996. His two other Chelsea goals came in their 1995–96 FA Cup campaign, with goals against Grimsby Town and Wimbledon. He won the League Cup, the UEFA Cup Winners' Cup and the European Super Cup with Chelsea, all in 1998, but faced stiff competition for a place in the side from the likes of Marcel Desailly and Frank Leboeuf. Duberry picked up an Achilles tendon injury in January 1997 meaning he missed the rest of that season, including the 1997 FA Cup Final.