Australian researchers believe a worm-like creature left a trail in sandstone found off the western tip of Australia.
If confirmed, it would be the oldest example of an animal comprised of more than one cell.
Until now, it was thought that multicellular animals, or metazoans, only appeared about 600 million years ago.
The rocks in question come from the Stirling Range Formation of south-western Australia.
Fine ridges in the sandstone may be "casts of mucus-impregnated strings of sediment left by an organism creeping over the surface," say Dr Birger Rasmussen and colleagues of the University of Western Australia.
Early world
The fossilised worm cast gives a glimpse into a primordial world.
This was a time when scientists believe the Earth was inhabited largely by microbes and algae.
According to current theory, there was a sudden burst of animal life about 600 million years ago.
This event - the Cambrian explosion - is clearly recorded in the fossil record.
There is little undisputed evidence of animal life before then, so the Australian research could prove contentious.
If the dating studies are correct, scientists will have to explain why little changed on Earth for millions of years after the arrival of primitive animals.
The fossil evidence is revealed in the journal Science.