The unnamed female calf was born to 12-year-old mother Sundara overnight after a 22-month gestation.
Keepers at the zoo said both mother and daughter are doing well and visitors will be able to see the new arrival from Saturday.
The calf is the 19th elephant to be born at Chester Zoo in its 85-year history and brings the current size of its herd to seven.
Five, including the new calf, are part of the same family called the Hi Ways.
Elephants are born into captivity in the UK only once or twice a year.
Keepers at the zoo watched the birth remotely via CCTV cameras so as not to disturb the herd.
The calf’s name will be decided in the coming days.
Richard Fraser, assistant team manager of elephants at Chester Zoo, said: “The arrival of a calf is a great family occasion for the elephant herd and brings the whole group together.
“As soon as Sundara began showing early signs of labour, you could see the rest of the family knew something special was about to happen.
“This was Sundara’s second pregnancy and the birth was pretty much perfect.
“She delivered her calf on to soft sand with all the family gathered around.
“Sundara then gave her a series of little kicks to gently stimulate and encourage her to her feet.
“Minutes later, the new arrival was up and standing and making her first attempts to suckle.
“There’s always a lot of excitement among the elephants whenever there’s a birth.
“It’s a hugely positive event for the herd.”
Asian elephants are native to South and South East Asia and are listed as endangered.
There are between 35,000 and 40,000 in the wild and managed breeding programmes.
They live to approximately 50 to 60 years old.
Mike Jordan, collections director at Chester Zoo, said: “Sundara’s new calf is a fantastic addition to the zoo’s Hi Way family of elephants and we hope that news of her arrival will generate more much-needed awareness of these incredible animals and the pressures for survival that they are faced with in the wild.
“In India, Asian elephants are regularly injured and killed in conflicts with humans.
“They wander into villages, destroying crops and property as they go, and this often results in forceful retaliation by villagers.
“Chester Zoo’s conservation work in Assam in northern India is, however, successfully helping to mitigate these problems, finding effective ways for people and wild elephants to live side by side.”