Yeah, an actual 'virus' is extremely rare. I've never seen one. Only heard of a few (and they are quite old - circa 1997).
Now, rootkits are a different story. Those exist. But they are generally run by a compromised root account - so it's not the same.
But back to linux virus (and in turn anti-virus)... So there are actually tons of linux anti-virus software out there. Most of the free windows ones offer a linux variant... and in fact, there is the awesome ClamAV for linux too. But fun fact, these are designed to check for windows malware. Yep. Turns out, tons of malware analysis is done collected and analyzed on linux machines.
But there is a cool new trend ... cross platform 'malware'. A few years ago there was an embedded macro in OpenOffice documents that would execute a different script based on the OS you were using. Cool stuff.
Linux virus? Yes, but no.