Petr Cech helped the Gunners enjoy a rare victory over Jose Mourinho's side on Sunday.
Olivier Giroud scored the decisive spot kick as Arsenal beat Chelsea 4-1 in a penalty shootout to win the Community Shield at Wembley on Sunday.
Arsenal and Chelsea were among seven teams to reach the Europa League knockout stage on Thursday, while last year's runners-up Olympique de Marseille were eliminated at the group phase.