The 34-year-old forward scored two stunning headers within three minutes to give Real Madrid a 2-0 lead before Kai Havertz reduced the deficit with a header near the end of the first half.
At the beginning of the second half, Benzema completed his hat-trick after capitalizing on a mistake by Edouard Mendy, making the score 3-1 at London's Stamford Bridge stadium.
Benzema recorded his first hat-trick in Real Madrid's 3-1 comeback win against Paris Saint-Germain in the last 16 round.
Real Madrid now have a big advantage heading into the second leg, which will take place at the Santiago Bernabeu Stadium on April 12.
In another quarterfinals first leg match, Villarreal beat Bayern Munich 1-0 thanks to Arnaut Danjuma's goal at home.
Villarreal will visit Bayern Munich at the Allianz Arena on April 12.
