Delhi Capitals sit at the top of the leaderboard having won two games from two.
CSK won the toss and elected to bowl, sending the Capitals in to bat first at Dubai International cricket stadium.
Prithvi Shaw led the charge for Delhi with 64 runs, earning him player of the match.
Delhi managed 175/3 in their 20 overs, before taking to the field.
Chennai Super Kings didn't manage to capitalise on the cooler innings, replying with 131/7, including Faf du Plessis' 43 from 35 balls.
Attention now turns to Kolkata Knight Riders versus Sunrisers Hyderabad on Saturday evening in Abu Dhabi.
After their first games, the two sides currently last and second-last in the standings, respectively.
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