Uruguayan forward Edinson Cavani found the net at the 78th minute to give PSG the edge at the Parc des Princes. Swedish striker Zlatan Ibrahimovic delivered the first goal, while Chelsea's equalizer was scored by Nigerian midfielder John Obi Mikel.
Mikel's goal keeps Chelsea's hopes alive for the second leg to be played at Stamford Bridge, London.
In the other match of the night, Portuguese club Benfica won 1-0 against Russian team Zenit Saint Petersburg in Lisbon. Benfica forward Jonas found net in injury time in the second half.
Zenit's Italian defender Domenico Criscito was sent off in the 90th minute.
Second legs will be played on March 9.
Chelsea will host PSG in London and Zenit will meet Benfica in the Russian city Saint Petersburg.
Results:
Paris Saint-Germain 2 - 1 Chelsea
Benfica 1-0 Zenit
Wednesday's fixtures:
Gent (Belgium) vs Wolfsburg (Germany)
Roma (Italy) vs Real Madrid (Spain)
