The tiny youngster, whose gender is not yet known, is only the second of the species to ever be born at Chester Zoo.
The baby will cling to its mother’s back for approximately six months until it is ready to walk, explore and find food on its own.
Parents Pedro and Bliss, both aged three, arrived in 2010 as part of an international breeding programme.
Team Manager David White said:“Bliss is a very good mum and is so far doing an excellent job of looking after her new arrival.
“She’s obviously very proud of her newborn and has, every now and again, been parading around and showing off to our visitors.
“Seeing the youngster clinging on tightly to her tail is quite the sight!”
Giant anteaters are classed as ‘vulnerable’ to extinction by conservationists and so the birth is good news for the unusual looking species.
Native to Central and South America the animals do not have teeth but have tongues which can measure up to half a metre long.