Chennai's skipper MS Dhoni put Virat-led team to bat first and restricted them to a low total of 70 runs in 17.1 overs.
For Bangalore, Parthiv Patel top scored with 29 off 35 balls.
After losing the match, Virat Kohli said, "No one wants to start like this, but it's good to get a game like this out of the way - this early in the tournament."
He further added, "We spoke of trying to be in the game, taking it to the 18th over was nice to see."
Kohli pointed out the flaws in the batting unit, saying, "The batting wasn't good, it wasn't easy to bat on, looked much better surface though, I thought 140-150 would have been an ideal score, especially with dew expected later on."
Harbhajan Singh (3/20 in 4 overs), Imran Tahir (3/9 in 3 overs) and Ravindra Jadeja (2/15 in 4 overs) shared the wickets. Dwayne Bravo also chipped in with a wicket. In reply, CSK scored the runs in 17.4 overs with Ambati Rayudu scoring 28.
Dhoni-led Chennai achieved the set target with 17 balls left.
Chennai have won their last six matches against Bangalore dating back to 2014 and at Chepak, Chennai have a 6-1 lead against Bangalore.
Chennai have won 12 out of their last 13 Indian Premier League clashes at Chidambaram Stadium.
After losing the match, Virat Kohli said, 'No one wants to start like this, but it's good to get a game like this out of the way - this early in the tournament.'