CSK, who have made a comeback to the cash-rich Twenty20 league after serving a two-year ban, will now play their six remaining home matches at the Maharashtra Cricket Association Stadium in Pune, the Governing Council said in a statement on Thursday.
The city will thus witness no more IPL action this season.
As the Chennai police also expressed their inability to provide adequate security for the remaining matches of CSK, the Board of Control for Cricket in India (BCCI) decided to shift the matches late on Wednesday.
While the venue shifts, the date of the remaining six matches remains the same.
"I trust a 'peaceful' resolution is found soon for the problems at hand. Thanks to everyone for making the team so welcome," Fleming added.
The Mahendra Singh Dhoni-led CSK side will face Kings XI Punjab in Mohali on April 15.
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