The out of sorts winger who was refused permission to leave Stamford Bridge in the summer netted with a fine low, drive on the stroke of half-time.
Celtic took an early lead through defender Gary Caldwell.
Chelsea announced at half-time that they have broken off talks with Arsenal over the transfer to the Bridge of Ashley Cole.
The full statement read: "Chelsea FC has been in discussions with Arsenal Football Club for some time over the possible transfer of Ashley Cole.
"Chelsea has made a very substantial offer for the player.
"Although discussions have continued, Arsenal's valuation of the player does not match Chelsea's and therefore no agreement can be reached in the current circumstances."
Chelsea offered £20m for the 26-year-old while Arsenal valued the player at £30m.
But Jose Mourinho has not ruled the deal as dead - just yet.
"I haven't lost patience, Ashley Cole is Arsenal's player and they have the power in their hands to say yes or no," he said.
"We have been looking all the time at other players. When you try to sign a player, you can't think this is the only player in the world you can get. You have to look at some alternatives.
"Of course he was an important choice for us but I believe he was also an important choice for them and they probably want to keep him.
"You will have to ask Arsenal if it will happen now. If I sign another left-back. I only want one more left-back. I don't want two. But there is a chance it will happen."
German international Phillip Lahm is top of the list should the Blues finally call Arsenal's bluff.
It would leave the north London side with a player who wants to get away but from a club who is unwilling to let him go cheap.
Sounds almost like the William Gallas situation.