Steve Cooper’s side were well worth Serge Aurier’s 63rd-minute equaliser after a spell of sustained dominance in the second half.
Raheem Sterling had scored a volley after 16 minutes to cap a good start from Graham Potter’s men, who eventually lost their way.
Pierre-Emerick Aubameyang, Hakim Ziyech, Conor Gallagher and Mateo Kovacic were all thrown on late but the draw leaves Chelsea in eighth place, seven points behind Manchester United in fourth.
Nizaar Kinsella was at the City Ground witnessing the first Blues game of the New Year...
Kepa Arrizabalaga - 6
Kepa made a good double save from Brennan Johnson in the first half and another good one in the second. There was little he could do with Aurier’s equaliser.
Cesar Azpilicueta - 5
The Blues captain became the club’s top overseas appearance-maker in his 495th outing for Chelsea. He did allow several counter-attacks to again fail to cover the absence of Reece James.
Kalidou Koulibaly - 6
With Monaco defender Benoit Badiashile soon joining for £33million, he showed good passing range to create Chelsea’s first chance for Mason Mount. He ended up being run ragged by a lack of protection in front of him.
Thiago Silva - 7
The 38-year-old produced moments of brilliance with the ball and in his defensive actions but was struggling for pace on a few of the counter-attacks.
Marc Cucurella - 6
Cucurella was solid enough and heavily involved defensively as the quickest defender in the backline.
Denis Zakaria - 7
After 60 minutes against Bournemouth, the Switzerland international showed that his release clause could yet prove value. He has hardly put a foot wrong in his limited displays for Chelsea but had to come off again on the hour mark as he builds fitness.
Jorginho - 4
The Italy international struggled to get into the game in the first half and found it tough in the physical midfield battle.
Mason Mount - 5
The 23-year-old was bright and combative but had moments where he got overpowered at the City Ground. He didn’t create enough when on the pitch and was taken off by Potter.
Raheem Sterling - 6
He reacted quickest for the opening goal after Willy Boly bizarrely flicked the ball onto his own crossbar. Matched some of Forest’s physicality but came off in the 72nd minute.
Kai Havertz - 4
After his goal and assist last time out, the Germany international had a quiet game and lacked any attacking impact. Moved into a deeper no10 role towards the end of the match.
Christian Pulisic - 6
Pulisic set up the first goal with a good bit of wide dribbling followed by a dangerous cross. He did, however, waste a good chance towards the end of the half. He was a bit weak in his defending for Forest’s equaliser.
Mateo Kovacic - 5
Came on for Zakaria in the 60th minute but had little impact after going deep into the World Cup with Croatia.
Conor Gallagher - 6
Played in an uncomfortable no6 role but added his physicality into a game in which Chelsea lost the midfield battle.
Hakim Ziyech - 7
Fresh after his heroics with Morocco at the World Cup, the winger looked revitalised, producing chances when he got the ball.
Carney Chukwuemeka - N/A
He wasn’t on the pitch for long enough to make an impact.
Pierre-Emerick Aubameyang - 6
The no9 came on in the 73rd minute with Ziyech and Gallagher. He couldn’t connect with Ziyech’s brilliant 80th-minute cross.
Unused subs: Bettinelli; Chalobah, Hall; Hutchinson.