The aristocrats have outplayed Southampton on penalties in the 1/8 final playoffs.
The main time of the game, which took place at the Stamford Bridge stadium, ended in a 1: 1 draw.
Kai Havertz scored for Chelsea (44th minute).
At Southampton - Che Adams (47th).
Rhys James scored the winning goal from the penalty spot.
The chief referee of the match, Kevin Friend, showed three yellow cards to the players of the Hampshire team.
Earlier it was reported that Arsenal beat Leeds in the 1/8 finals of the League Cup.