Christian Pulisic got the Blues off to a dream start - albeit after Timo Werner had already missed a golden chance - with what could yet prove a crucial away goal, but Karim Benzema equalised for a sub-par Madrid shortly before the break to leave the tie finely poised.
Chelsea will take a slight advantage into the second leg of their Champions League semi-final with Real Madrid, after the first leg in Spain ended in a 1-1 draw.
Pulisic's season hasn't gone totally according to plan as injuries and the arrivals of Timo Werner, Kai Havertz and Hakim Ziyech have made it difficult to carve out a place in Chelsea's starting XI. But the 22-year-old displayed how he continues to be a potent attacker by becoming the first American to score in a Champions League semifinal tie.
Collecting a pass from Antonio Rudiger on the edge of the 18-yard box, Pulisic's momentum took him to the left of the goal. The Pennsylvanian cut back to his right and eluded former Chelsea keeper Thibaut Courtois before giving the Blues a 1-0 lead in the 14th minute.
Despite being the stronger side in the first half, Chelsea was unable to maintain its advantage before halftime.
