The 18-year-old has already represented the club's Under-23 side in the Checkatrade Trophy this season, and he has now been given the opportunity to continue his development in League One for the final four months of the campaign.
Manager Karl Robinson told the club's official website: "Jay is somebody who has been very highly thought of in Chelsea's academy system over the last three years or so. What he'll give us is a real dynamic speed and a real agility in his movement.
"He's a left-footed player that can play as a winger, a wing-back and in the number 10 position. Technically, he is outstanding and we are very pleased to get this deal done right away.
"We are short on bodies at the moment and Jay will help to bolster our squad, as well as the move aiding his development."
The England Under-19 international is available to make his debut against Bristol Rovers on January 2.