Chahar, who was back at the team's bio-bubble on Wednesday after returning two negative tests, had to undergo a cardio-vascular test as per BCCI protocol before he could hit the nets.
"He will start training from today. He has got necessary clearance from BCCI," CSK CEO Kasi Viswanathan told PTI. "The team is training hard and in good shape. We are looking forward to our first game."
Last year's runners-up CSK face defending champions Mumbai Indians in the opener on September 19.
Another player, a batsman, who was tested positive shortly after team's arrival in Dubai, will be tested on Saturday.
CSK were the last team to start training in the UAE after 13 members of their contingent had tested positive. They will also be without Suresh Raina and Harbhajan Singh who have both pulled out of the tournament for personal reasons.
"We will miss our senior players but at the same time, it is an opportunity for others to stand up and prove themselves," Viswanathan said. "We are confident of doing the job well with what we have."