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 SPFL has set up a working group to examine the issue of unacceptable conduct.
And it is understood that they would seek financial assistance from the Scottish government.
The facial recognition system was mentioned at a meeting of all 42 clubs on Tuesday.
The debate over the extent to which clubs should be held accountable for the conduct of their followers has been sparked by recent incidents involving Rangers, Celtic and Dundee United supporters.
Hibernian's visit to Ibrox on 28 December was marred by sectarian chants from the home end, while there were complaints of sectarian songs during Celtic's Scottish Cup trip to Stranraer.
Celtic and Dundee United have both condemned their own fans for setting off pyrotechnics.
SPFL board member Mike Mulraney revealed there was not appetite to introduce new strict liability rules.
The Alloa chairman said there is "no chance whatsoever" of clubs agreeing to regulations that could see them punished for the conduct of supporters regardless of whether the club itself is to blame.
A spokesman for the league body said: "The SPFL is working with government and other partners with the aim of establishing a workable solution to help rid our football grounds of unacceptable conduct.
"This work is at an early stage and is not being led by any one club.
"The issue of unacceptable conduct is something that the SPFL, its board and its member clubs are absolutely committed to addressing.
"Recognising that certain behaviours are for society to face and address as a whole, we believe football can take a leading role in moving this issue forward for Scottish society."
The prospect of facial recognition technology has been met with scepticism from the Scottish Football Supporters' Association.
Chairman Simon Barrow said the fans' group is concerned by "a rushed move towards intrusive surveillance".
He added: "There needs to be careful consultation with fans and clubs, alongside wider consideration of how to deal effectively and proportionately with threatening and insulting behaviour.
"The best way forward will involve working with the great majority of supporters who deplore such abuses, rather than making them feel under accusation themselves."

Shelly Wu, six, and Lily, seven, were hit near the Grove Lane and Antrobus Road junction, Handsworth, last June.
Michael Junior, 35, from Handsworth, admitted two charges of causing death by dangerous driving and three charges of causing serious injury by dangerous driving, at Birmingham Crown Court.
Junior will be sentenced at the same court on Thursday.
The crash caused serious injury to Shelly and Lily's mother, Zhulan Wu, and her other two children.
More on this story and others on Birmingham and Black Country
Sgt Steve Newbury from West Midlands Police said: "This tragedy rocked the local community and devastated a family. Lily and Shelly's mum continues to recover from serious head injuries."
He added the children who survived have recovered from their injuries but continue to suffer "emotional trauma".
Judge Murray Creed imposed an interim driving ban on Junior, of Copthall Road, and granted him bail until Thursday, when he will reappear in court.
The birth of an elephant calf has been captured on CCTV at Chester Zoo.
[NEXT_CONCEPT]
The Scottish Professional Football League is considering the use of facial recognition technology at stadiums to help combat anti-social behaviour.
[NEXT_CONCEPT]
A man has pleaded guilty to causing the deaths of two sisters in a road crash in Birmingham.