The nine-week-old twins were born on Saturday, 22nd June to mum, Nima and dad, Koda who have kept them tucked up in their nest boxes since birth.
Now, specialist vets have had their very first look at the duo, classed by conservationists as endangered in the wild, when they examined the pair during their first health check.
Speaking about the new arrivals, James Andrewes, Assistant Team Manager at the zoo, revealed that the siblings are doing very well under the watchful eye of their parents.
"Happily, both cubs are developing very well indeed and the health MOTs we've been able to perform confirmed that mum Nima is clearly doing a great job of caring for them."
Adding: "We also discovered the genders of each of the cubs - one male and one female - and returned them to their mum as soon as we'd finished giving them a quick once over.
"Nima took them straight back to her nest and it'll be a few weeks now until the cubs start to develop the confidence to come out and explore by themselves.
"Before they're able to stand on their own feet, it is though possible that some lucky people will have the occasional glimpse of Nima carrying them from nest to nest by the scruffs of their necks," he remarked.
Red pandas are found in the mountainous regions of Nepal, India, Bhutan, Myanmar and southern China where their wild population is estimated at fewer than 10,000 - a 40 percent decline over the past 50 years.
This decrease is a direct result of human actions, such as widespread habitat destruction, trapping for the illegal pet trade and poaching for their red fur.
In recent years, Chester Zoo has been fighting for the future of the red panda, which is also known as the 'fire fox', through habitat-focused conservation projects in the Sichuan Mountains of China, where they can be found among the bamboo forests.
Conservationists at the Zoo have recently called on people's help to fight the illegal wildlife trade.
Members of the public can report any suspicious activity they may spot, online or on holiday, via the zoo's online illegal wildlife trade reporting form here.