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CSK are already without opener Devon Conway as the Kiwi batter has been ruled out for at least the first half of the league.
The 32-year-old Conway will undergo surgery on his left thumb which got injured during the second T20I in Auckland on February 23.
Conway broke his hand as New Zealand defeated England on Wednesday to reach the final of the Twenty20 World Cup.
Tim Seifert will replace Conway in Sunday's final against Australia.
Conway has also been granted an exceptional circumstance dispensation by the ICC, which means should he be selected for New Zealand's tour of Bangladesh starting on August 12, he would be allowed to play tour matches before the deadline of August 28.
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