Sutton was sold to Chelsea for £10 million after Blackburn's relegation. His time at Stamford Bridge proved an unhappy one, as he struggled both to live up to the price tag and to adapt to Chelsea's style of play, scoring just one league goal in a 5–0 win against Manchester United in 28 appearances, and three goals in total, the other two coming against Skonto Riga in a Champions League qualifier, and Hull City in the FA Cup. He failed to even make the bench for the club's FA Cup Final win against Aston Villa, and was sold to Scottish Premier League side Celtic for £6 million in the summer of 2000.