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22 August 2015 Last updated at 12:18 BST
After a pregnancy lasting 22 months, Thi Hi Way, a 34-year-old Asian elephant at the zoo, gave birth to the female on Thursday afternoon.
Zookeepers said the calf, which is yet to be named, was on its feet within three minutes and is doing well.
The birth of an elephant calf has been captured on CCTV at Chester Zoo.