Can the third generation Apple TV run tvOS?

Older Apple TVs will not run tvOS.

Unfortunately, the third generation Apple TV can not run tvOS. This is due to hardware limitations - the older Apple TV has an A5 processor while the new fourth generation Apple TV is equipped with the A8. So your older Apple TV won't support Siri, the App Store or third party controllers. That said, Apple will likely continue to update the software for the third generation Apple TV, as it continues to be an affordable option at $69.