Yep, you'll hear them out back clucking the words to "I'm My Own Grandpa". Chickens do not care if they're kissin' cousins or not, and their eggs ARE fertile.
If it continues in successive generations, chickens from that union may have problems eventually, chicken generations are pretty short, not like humans where it's 15-20 years apart, a chicken generation can be a year apart! The first generation won't get too funky though, at least that's my observation, and sometimes you want it to some extent...
BUT Maybe we need a thread about how we avoid it if we're not trying to line breed on purpose.
My solution was to, cull my roos and trade one or two with friends to get new blood in, AND, to periodically buy or trade eggs for my broodies to hatch that were not at all related to my roo so he could stay around if I liked him.