Branislav Ivanovic headed Chelsea into the lead after 36 minutes but Edinson Cavani replied for PSG shortly after half time.
The home side looked more likely to grab a winner but Cavani prodded a shot just past the post and Thibaut Courtois saved Zlatan Ibrahimovic’s injury-time header.
The two teams will meet again in the second leg at Stamford Bridge on March 11.
Jose Mourinho will be hoping for more from his side in the return leg as they were largely second best in Paris, particularly after the break.
Diego Costa was recalled for Chelsea after returning from his three-match suspension while Courtois, Gary Cahill and Cesc Fabregas also started for the visitors.
The Blues had won just once in six prior attempts on French soil and were beaten 3-1 on their last visit to Paris in the quarter-finals of the Champions League last season.
On that occasion the deadlock was broken inside the opening five minutes, but that never looked likely on Tuesday night.
Neither side showed much attacking desire in the early stages, but it was the hosts who created the first chances in the 10th minute as Blaise Matuidi and Ibrahimovic both had headers palmed away by Courtois.
The Belgian, preferred over Petr Cech, was called into action again after half an hour to keep out a near-post header from Cavani.
But despite looking more threatening, PSG fell behind after 36 minutes as three defenders combined to give Chelsea the lead.
Gary Cahill showed a neat touch to flick John Terry’s cross on for Ivanovic, who headed into the corner and out of Salvatore Sirigu’s reach.
Chelsea looked comfortable after the goal and at the break it seemed as though they were halfway towards a near-perfect away display.
However, PSG came out with more attacking intent in the second half and equalised in the 54th minute as Cavani was given too much space in the box to head home Matuidi ‘s left-wing cross.
Buoyed by the goal, the hosts went close to taking the lead shortly afterwards when Ibrahimovic saw a shot saved after slaloming into the box and then Ezequiel Lavezzi’s follow-up was blocked.
Chelsea weathered the immediate storm but PSG came again and Cavani almost made it 2-1 when he glided into the box, wrong-footed Nemanja Matic and prodded narrowly wide of the post.
The Uruguayan then missed an acrobatic scissor kick from Javier Pastore’s high cross as the hosts pressed for a winner.
Chelsea offered little themselves at the other end and almost conceded in injury-time as Courtois did well to palm away Ibrahmovic’s downward header.
However, in the end the spoils were shared and the Blues will be favourites to progress to the last eight when the sides meet in London next month.