So, Manchester United will start 2016 without a win in eight league and cup games. Will they be starting it with a new manager at the helm? Thanks for your company. We're back on Tuesday to see if Leicester City can return to the top of the Premier League table by beating Manchester City. Don't forget you can catch up on all of today's action on Match of the Day which is on BBC One at 22:30 GMT.
- Man Utd miss host of chances
- United in sixth place on 30 points
- Chelsea up to 14th on 20 points
BBC Sport chief football writer at Old Trafford
"United's vibrant start, out of character with the timidity of recent weeks, instantly lifted the spirits and the fans remained solidly behind their team throughout. The final whistle was greeted with some jeers but this was more out of frustration that United could not find a winner."
Manchester United manager Louis van Gaal speaking to BT Sport: "It was a very good performance but you have to score - we didn't. Two times we hit the post with goalkeeper beaten. We also have big chance in the second half, two penalty cases and didn't receive penalties. We are forcing the luck but we don't have the luck that we need."
BBC Sport chief football writer at Old Trafford
Chelsea interim boss Guus Hiddink says in his news conference: "The players have experienced a very bad half year. They have to lift it up and that's what we have talked about in the locker room. Everyone is convinced we couldn't go on on the same path and we have shown that in the last three games."
Manchester United manager Louis van Gaal speaking to BBC Sport: "We have forced the luck and still we didn't score and that is unbelievable when you see what happens today. I am frustrated.
"I thank my players for the performance but we need a victory. It gives a lot of hope for the fans. My relationship with players, board and staff members is very good. There is no reason to sack me.
"The results are not good enough. I know that, the players and board know that. It can be different in about one month."
Manchester United midfielder Morgan Schneiderlin:"I thought we were unlucky. Everyone in the changing room is disappointed we did not win. We dominated the game and had a good tempo - we were on the front foot from kick-off and showed commitment.
"We wanted to show the fans we wanted to win but it is the same story again - in football you can't win if you don't score."
Chelsea manager Guus Hiddink, speaking to BBC Sport: “On the one hand, I am happy with a point because we had a difficult game, but on the other, we had two big chances to get three points. We were lacking some attacking players and had to adapt. In general, I’m happy.
“Hazard is very mobile and can go either way. His preference is the left and he’s doing very well in the centre. All our strikers are injured, so we have to adapt."
Next up for Chelsea is fifth-placed Crystal Palace away on 3 January. The champions start 2016 three points above the relegation zone and 14th in the Premier League table.
Manchester United manager Louis van Gaal, speaking to BT Sport: “For me, it [his future] is not an interesting subject because I cannot have any influence on that, I can only work with my players and you can see they are fighting for me. Even after this result the fans were applauding so I cannot say I’m very much concerned. In this football world you never know, but I’m fully confident in the board and my players.
"Will I resign? On the contrary. When the players can give such a performance with a lot of pressure, there is not any reason to resign for me. Maybe the media wants me to but I shall not resign. It's not a question of staying, it's a question of fulfilling my contract."
Wayne Rooney says he has apologised to Oscar for his high challenge towards the end of the game. The United captain escaped with a booking.
Louis van Gaal tells BT Sport he is not going to resign. More from the Manchester United manager coming up.
Chelsea goalkeeper Thibaut Courtois, speaking to BT Sport: “They wanted to win in front of their fans. From the start they put high pressure on us. Without a striker, it wasn’t easy for us to find depth but we had chances and David [de Gea] played well. The team showed progression, which was good.
“It’s a pity Matic doesn’t score. It’s more difficult for us than last year, but I think we are getting into a flow to win games.
“You cannot think it’s not possible to get relegated, but we look forward, and we think that soon we will get the winning flow.”
United had 67% possession to Chelsea's 33% yet they end 2015 without a win in eight league and cup games. They will start 2016 out of the Champions League, League Cup and nine points behind new Premier League leaders Arsenal.