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 was doing well.
Andy Mckenzie, team manager of elephants at Chester Zoo, described the "very smooth" birth as a "real family occasion".
He said: "They all knew that something was going to happen, especially the older elephants that have seen it all before.
"It was great to see the younger individuals being around the birth and learning from the older cows in the family."
Asian elephants
Source: Chester Zoo
The birth of an elephant calf has been captured on CCTV at Chester Zoo.