Jeev Milkha Singh (70-79) and Gaganjeet Bhullar (74-73) had missed the cut.
Justin Rose, who had rounds of 67 and 69, was four-under through 11 holes in third and was 12-under with seven holes to go. He was in clear lead with Thongchai Jaidee (66) the clubhouse leader at nine-under.
Thorbjorn Olesen was nine-under but had six holes to play in third round.
Chowrasia, who has had very modest success on the European Tour since his 2011 win at the Avantha Masters, seemed to be returning to form after his win in the Indian Tour event in December.
"I had been playing well but there was a niggling wrist injury but that seems to getting better and I am more confident," said Chowrasia. "Here in Abu Dhabi it is a long course, but if you hit straight it is fine and I managed that today. On the first two days I did get my birdies but I also made some mistakes."
Speaking of his confidence, he added, "The win in India helped and I have been hitting quite well, though last week again I felt I was troubled but right now things seem fine." More