PSG are on 69 points with four games left with Monaco trailing by 11 points
Aaron Ramsey's 79th-minute header sealed victory for Arsenal, three minutes after Diego Costa's equaliser had revived Chelsea's hopes of capping a superb season in style.
Alexis Sanchez's controversial opener had given Arsenal the early initiative and Arsene Wenger's side could have been further ahead as they dominated the first-half chances.
Chelsea improved after the break but had to play the final quarter of the match with 10 men after Victor Moses received his second yellow card following a blatant dive in the area.