I've had my veiltail, Enjolras, for a few months and have never had a problem with him biting his tail before. But today, I saw him flaring at himself and chasing his tail - and there were pieces of it missing. He's chased his tail before, but I never noticed pieces missing like this.
He lives by himself in a 2.5g that's heated and filtered. Sorry I couldn't get a better picture, he was moving too quickly for me to get a good shot. If you can't really see the damage, I'll try and get a better shot.