The kits (baby Squirrels), a boy and three girls, were successfully bred at Longleat as part of a UK-wide programme to reintroduce the species back into the wild.
The rodent, last seen in the county in 1965, is virtually extinct in England.
Keeper Chris Burr said, “I came in one day and there was mum, dad and an extra little head, and by the afternoon they just poured out, it was fantastic.”
Mr Burr said the Squirrels were born blind, deaf and hairless a few months ago.
“We don’t have names just yet, they’re still quite young but they’re growing up really, really fast,” he added.
Totally dependent on their mother for the first 10 weeks of their lives, Mr Burr said she had been “fantastic”.
“Mum is an absolute legend,” he said.
“She built this nest called a breeding dray, it’s the size of a football, and she was extremely protective of it and that’s when we knew something was going on.”
Once fully grown, the family of kits will become part of future breeding programmes or may be released into the wild.
“Obviously our ultimate goal would be to have a population living on the Longleat estate,” said Mr Burr.
“How cool would it be in 10 to 15 years time to have these little red fluff balls just bouncing around Longleat – that would be fantastic.”
Red Squirrels were widespread across most of the country until the 1940s, but there are now only 140,000 Red Squirrels in the UK, compared with two-and-a-half million of the grey variety.