Christian Pulisic has become the first American to score in the Champions League semi-finals but an acrobatic equaliser from Real Madrid's Karim Benzema left their tie delicately balanced at 1-1.
The Blues could have come away with a victory on a sodden night at the Alfredo Di Stefano stadium but Timo Werner spurned two fantastic chances.
In the first Champions League match since the controversial European Super League folded last week amid widespread criticism, Chelsea got off to a fast start and had chances to add to their lead after Pulisic opened the scoring with a nice finish in the 14th minute.
It was the first goal conceded by Real goalkeeper Thibaut Courtois in six hours and 44 minutes.
Thirteen times European Cup winners Real looked ragged and short on ideas but pulled level in the 29th with a moment of true class from the talismanic Benzema.
Chelsea looked the better side in the second half as well but could not break down Real again and then had to withstand some late pressure from the hosts, who visit Stamford Bridge in the second leg on May 5 looking to reach the final for a fifth time in eight years.
Manchester City host Paris Saint-Germain in the other semi-final first leg on Wednesday.
Real struggled early after a quizzical switch to three at the back for the visit of the Blues.
Werner should have scored before the game had even settled but instead he side-footed straight at Courtois.
Pulisic's unselfish header across goal begged to be blasted into the net but Werner's tentative effort handed the ex-Chelsea keeper the chance to parry clear.
Pulisic was in no mood to waste his own opening, however.
Antonio Rudiger's lofted ball caught Real out at the back, allowing Pulisic to spring whatever offside trap there was, power into the box, step round the on-rushing Courtois and powering the ball home.
Benzema produced the first threat for Real however, thundering a 20-yard effort against a post.
And the French striker then conjured an equaliser of the highest quality just before the half hour, cushioning a header to himself six yards out - then flashing a snap volley past the helpless Edouard Mendy.
Had Werner connected with Pulisic's teasing cross, Chelsea would have taken the lead again.
The Germany forward still found time to screw a shot wide of the near post when Mason Mount was lurking in the centre of the box.
"We should have scored a minimum one more (goal) in the first half. We had good control and good attacks. We were very confident and looked very strong," Blues manager Thomas Tuchel told BT Sport.
"The second half was a very tactical game, the speed and intensity dropped and we are a little bit tired."