The Blues had to settle for a draw in Germany but they have the advantage of an away goal ahead of the second leg of their Europa League semi-final tie at Stamford Bridge.
Frankfurt made a strong start and broke the deadlock midway through the first half with a swift counter.
Olivier Giroud lost possession, and the Bundesliga club surged forward with Luka Jovic finishing off the move by flicking Filip Kostic's cross in off the post with a headed effort.
Chelsea responded well and grabbed a potentially crucial away goal just before the break. Ruben Loftus-Cheek picked out Pedro after Frankfurt were unable to clear a corner, and the Spanish forward took one touch then hammered the ball home.
The visitors looked the more likely to score again after the restart and David Luiz forced a good save from Kevin Trapp in the Frankfurt goal from a free kick.
Eden Hazard, who entered the action with 30 minutes to play, nearly produced a winner as he picked out Luiz from a free kick but the defender's header was straight at Trapp.
There were a few nervy moments for Chelsea late on as David Abraham headed over from a corner and Luiz blocked a goal-bound Goncalo Paciencia effort after Chelsea had been caught in possession deep in their own half.
Chelsea set a new record of 16 games unbeaten in the Europa League with the draw and will be confident of securing a spot in the final ahead of next week's second leg in London.