Japanese marine researchers have found and successfully filmed the young fish at a depth of 528ft in Manado Bay off Sulawesi Island, Indonesia.
Video footage shows the 12.6-inch coelacanth, coloured blue with white spots, swimming slowly among rocks on the seabed for about 20 minutes.
Researchers used a remotely operated, self-propelled vehicle to film this rare baby coelacanth
As far as we know, it was the first ever video image of a living juvenile coelacanth, which is still shrouded in mystery,' said Masamitsu Iwata, a researcher at Aquamarine Fukushima in Iwaki, northeast of Tokyo.
Scientists hope the discovery will shed light on the habitat and breeding habits of coelacanths.
The researchers used a remotely operated, self-propelled vehicle to film the coelacanth, which appeared to be newly born, Iwata said.
A similar-sized juvenile was once discovered in the belly of a pregnant coelacanth. It is believed that their eggs hatch inside the female and the young fish are fully formed at the time of birth.
Coelacanths are commonly regarded as having evolved little from prehistoric times and were thought to be extinct until a living specimen was discovered in 1938 off the coast of southern Africa.