Brett Lee struck in his first over to remove Faf du Plessis cheaply. Du Plessis failed to continue his good run as he scored three runs before going back to the pavilion.
Earlier, Chennai skipper Mahendra Singh Dhoni won the toss and opted to bat against Kolkata in the 41st of the tournament.
Kolkata decided to retain the same playing eleven that thrashed Royal Challengers Bangalore by 47 runs.
Both the teams are meeting this season for the first time and the Gautam Gambhir-led KKR hold the advantage after having won five of their nine matches so far.
Comparatively, Chennai are faltering because of their batting woes and lost by seven runs to tournament laggards Kings XI Punjab on Saturday.
Gambhir has been leading from the front and his batting this season in particular has been spectacular. The manner in which he tamed the Royal Challengers Bangalore at home on Saturday with a 51-ball 93 was intimidating sight for any opposition bowler.
Same cannot be said about CSK captain Dhoni, who has been under the mat for months now. His personal contribution with the bat for both the national side and now for the Super Kings has been below par.