Chacarra was four shots off the lead after two rounds, then carded a 68.
McIlroy will play the final round alongside Englishman Dan Bradbury, who climbed to four under with a 66.
The round also carries a wider prize. McIlroy will clinch the title if he finishes ahead of Chacarra and in the top four.
McIlroy had taken the outright lead with an eagle three on the par-five seventh. Bogeys on the eighth, ninth and 10th then wiped out that advantage.
A birdie on the 14th was followed by another dropped shot on the 15th. He finished with a birdie at the par-five 18th after narrowly missing a six-foot eagle putt.
Hatton's finish was a scramble. He made par at the last after driving into the water and finding a greenside bunker with his approach shot.
"It would mean a lot to go on and win tomorrow,"Hatton said.
The 68 included nine birdies, three bogeys and a double bogey.