The England U21 international, who can play at centre-half or in central midfield, will stay at Turf Moor until January.
Chalobah built a reputation as part of two FA Youth Cup-winning sides at Chelsea but is yet to appear for the club's first team.
The 19-year-old has previously been on loan at Watford, Nottingham Forest and Middlesbrough.
Burnley manager Sean Dyche told his club's official website: “Nathaniel is someone we have been interested in for a while. I’ve followed his career journey and he did tremendously well at Watford, then had an indifferent last year, but I think players grow from that.
“My way of looking at developing players is not the same as anyone else. You have to take the rough with the smooth as you are developing as a young player and I think he has come out of that more rounded.
“I’ve had a chat with him and enjoyed speaking to him and I think he has something to offer us.
“He knows the challenge and he knows the strength of our midfield, in particular with David Jones and Dean Marney, and he was willing to take that on.
“He is very well thought of as a player, an England U21 international and we want a mix in the group of older players who have been round a bit and the freshness and lack of inhibitions to go out and play.
“He thinks this will be a good environment for him, which I do too.”
Another young Chelsea striker, Islam Feruz, has joined Greek side OFI Crete on a season-long loan.