After opting to bat, CSK were off to a good start with Murali Vijay (31) and Michael Hussey (26) compiling a solid 61-run stand before Vijay was run-out against the run of play.
After Vijay was run out by Ben Rohrer, one over later, Michael Hussey too departed as Virender Sehwag took a neat catch in the deep.
Ravindra Jadeja (24) joined MS Dhoni in the middle as the duo compiled a 57-run stand in 32 balls.
MS Dhoni scored an unbeaten 58 off 35 balls propelling Chennai to 168 for 4 in their allotted 20 overs.
Chasing 169 to win, Delhi started off badly again losing Virender Sehwag for 0 in the 2nd ball of the innings. Mohit Sharma was the wicket-taker.
After Sehwag's early departure (0), Chand and Botha combined for a 34-run stand, but both of them perished in quick succession followed by Jadhav and Rohrer as Delhi slumped in chase of 169.
Albie Morkel was the pick of the CSK bowlers as he finished with figures of 4-0-32-3, with Chennai winning the tie by 33 runs.
Delhi captain David Warner stuck around for a while but with his team going down hill, losing wickets at regular intervals his lone battle of 44 runs could not revive his team.