Chelsea's dreams of winning a first-ever Women's Champions League title hang by a thread after losing 3-1 to rivals and holders Arsenal in the first leg of their quarter-final. Both sides' flailing Women's Super League campaigns means the importance of their European exploits have only increased, and it is the Gunners who hold the advantage heading into next week's second leg at Stamford Bridge.Chelsea, shorthanded by various injury and fitness concerns, went close to going in front inside seven minutes when Lucy Bronze released Alyssa Thompson down the right flank, with the American winger cutting inside and seeing her shot deflected onto the post by Laia Codina. The early pressure continued as Lauren James scampered away from Codina and found room for a shot, but she was denied by the same post that Thompson struck just moments beforehand.But against the run of play, Arsenal broke the deadlock. Katie McCabe free-kick found the head of Stina Blackstenius, who got between Erin Cuthbert and Keira Walsh to nod beyond a helpless Hannah Hampton.Chelsea found themselves two down on 32 minutes. A neatly-worked move ended with Chloe Kelly freely picking up the ball 25 yards from goal, and her speculative effort swerved under the arms of Hampton and in.The Blues had the ball in the net just before the break when Veerle Buurman got above Codina to head in from a free-kick after Kadeisha Buchanan's flick-on took goalkeeper Anneke Borbe out of the game. However, the referee blew the whistle for a supposed foul by Buurman, and inexplicably, the VAR did not see a reason for an on-field review, causing a stir on the touchline.With 25 minutes remaining, Chelsea pulled one back in outrageous fashion. Arsenal thought they had cleared their lines from a corner, but James popped up 25 yards out and picked out the top corner with a sensational shot on her weaker left foot that was half-dinked and half-driven.However, that reprieve was short-lived as Arsenal extended their advantage back to two again. A swift counter attack saw Buchanan step up to try and press Blackstenius, who instead slipped the ball in for Alessia Russo to lash in.James brought Borbe into a fine save with another superb attempt from distance as Chelsea tried to narrow the deficit again, and they saw another goal ruled out for a foul after Buchanan kicked the Arsenal goalkeeper to force the ball over the line from a corner. Down the other end, Johanna Rytting Kaneryd made a vital goal-line clearance to keep out Lotte Wubben-Moy as a back-and-forth first leg ended 3-1.GOAL rates Chelsea's players from the Emirates...Hannah Hampton (4/10):Probably should have done better to keep out Kelly's long-range strike which knocked the stuffing out of Chelsea and gave them a mountain to climb if they're to avoid elimination from the Champions League.Lucy Bronze (7/10):Affected the game so delicately with her experience and quality, expertly knowing where to position herself and who to bring into play at any given time.Naomi Girma (6/10):Wasn't afraid to try and open Arsenal up with her adventurous passing. Subbed for winger Rytting Kaneryd as Bompastor shuffled the pack.Kadeisha Buchanan (5/10):Soldiered on for the full 90 after overcoming an early hamstring scare. Afforded Russo the opportunity to score Arsenal's third by pushing high and engaging Blackstenius. Had a late goal ruled out after the follow through of her shot caught Borbe directly in the midriff.Veerle Buurman (6/10):Cruelly denied her first Chelsea goal by an extremely harsh referee and VAR call before half-time, seemingly being punished for jostling with Codina. Finished the game at centre-back.Keira Walsh (4/10):Lost the run of Blackstenius leading to Arsenal's opener, while Russo often found space to operate in behind Chelsea's starting No.6.Erin Cuthbert (5/10):Bounced over the pitch with energy, winning the ball back and creating openings with her pressing alone. Not as effective in possession. Taken off for Kaptein.Sjoeke Nusken (5/10):Similarly found herself in action across every blade of grass. All three Chelsea midfielders lacked the composure needed to calm the game down when Arsenal were in the ascendancy, however.Alyssa Thompson (7/10):Chelsea's spark on both flanks, using her acceleration and quickness well to stretch and panic Arsenal. Unlucky not to have grabbed the tie's first goal having seen her effort blocked onto the post.Lauren James (8/10):A ludicrously gifted footballer and the best player on the pitch. Put in an eye-catching performance in the final third even before she fired into the top corner of the Arsenal goal.Sandy Baltimore (5/10):Couldn't find a way to impact the game from open play as a winger and was moved to left-back following Rytting Kaneryd's introduction.Add GOAL.com as a preferred source on Google to see more of our reportingJohanna Rytting Kaneryd (6/10):Replaced Girma, bringing fresh legs to attack and providing more balance in the final third than Baltimore.Wieke Kaptein (N/A):Introduced late on for Cuthbert.Sonia Bompastor (6/10):Didn't have much room for manoeuvre with a depleted squad, while Chelsea did broadly play well. They do have an uphill battle to reach the semi-finals now, however.