moved nine points clear at the top of the Premier League as they extended their
winning run to 11 games with a 1-0 victory at Crystal Palace.
Diego Costa scored the only goal of the game, heading home Cesar Azpilicueta's cross in the 44th minute to score his 13th league goal of the season.
The visitors, who will be without both Costa and N'Golo Kante for the Boxing Day fixture against Bournemouth after the pair picked up yellow cards, pushed for a second with substitute Cesc Fabregas and Marcos Alonso both being denied by Wayne Hennessey saves.
Alonso then struck the crossbar with a free-kick in the 84th minute but the wasted chances did not prove costly as Antonio Conte's side held on for a third straight 1-0 win to extend their lead at the top, and equal a club-record run of successive wins.
Palace, who have just one win from their last 11 games, remain 16th, three points above the relegation places.
Eden Hazard returned to Chelsea's starting line-up alongside Nemanja Matic, while Jason Puncheon and Joe Ledley came in for Palace as both sides made two changes from their midweek fixtures.
In foggy conditions at Selhurst Park, it was a scrappy affair with chances few and far between until Yohan Cabaye picked out Martin Kelly in space on the right flank. The full-back's low cross was met by Puncheon, but he scuffed his shot wide.
There was a blow for Chelsea in the 22nd minute when Costa's clumsy tackle on Joe Ledley resulted in a yellow card, which rules him out of his side's clash with the Cherries at Stamford Bridge.
The tackles continued to fly in with Costa on the receiving end of a strong but fair sliding challenge from Cabaye as Palace continued to disrupt the visitors' rhythm.
Palace then had another sighting of goal as Kelly's cross picked out James McArthur but the midfielder's header flew wide.
It proved to be costly as Chelsea took the lead just before the break as Costa rose above Scott Dann to head the ball back across Hennessey and into the back of the net.
After the break, Chelsea looked to make the game safe with a second goal but Kante's swerving shot was parried by Hennessey.
Kante then picked up a booking which will rule him out of Chelsea's clash with Bournemouth, before Alonso's volley hit the side netting to a second goal.
Substitute Fabregas then shot straight at Hennessey before the Welshman dived full stretch to tip Alonso's powerful drive away.
The closest the visitors came to extending their advantage was in the 83rd minute when Damien Delaney fouled Hazard on the edge of the area. Alonso stepped up and curled a free-kick against the underside of the crossbar.
A second goal was not forthcoming but it was never truly needed. The home fans were buoyed by five minutes of added time but Chelsea held on for victory as they head into Christmas with a healthy lead at the top.
Crystal Palace: Hennessey (7), Ward (6), Dann (6), Delaney (7), Kelly (7), Zaha (7), Cabaye (7), McArthur (6), Ledley (6), Puncheon (6), Benteke (5).
Subs used: Fryers (n/a), Townsend (5), Campbell (5).
Chelsea: Courtois (6), Azpilicueta (8), David Luiz (7), Cahill (7), Moses (7), Kante (8), Matic (7), Alonso (7), Willian (7), Diego Costa (8), Hazard (7).
Subs used: Ivanovic (6), Fabregas (7), Batshuayi (n/a).
Man of the Match: Cesar Azpilicueta
Crystal Palace Hennessey, Kelley (Fryers 83), Dann (c), Delaney, Ward, McArthur, Ledley, Zaha, Cabaye (Campbell 78), Puncheon (Townsend 76), Benteke
Subs Not Used Speroni, Lee, Mutch, Husin
Booked Ward, Delaney
Chelsea Courtois, Azpilicueta, Luiz, Cahill (c), Moses (Ivanovic 78), Matic, Kante, Alonso, Willian (Fabregas 63), Costa (Batshuayi 88), Hazard
Subs Not Used Begovic, Zouma, Pedro, Chalobah
Booked Costa, Kante, Fabregas
Goals Costa 43
Referee Jon Moss