It's called Carali's, and in the true Louisville tradition of giving locations by what was previously housed in the building, it's in the former Shah's Mongolian Grill spot in the Stony Brook shopping center (near HH Gregg and Buffalo Wild Wings)
According to this page:
http://caralischicken.com/contact-us/4678583 they are open daily 11 am to 10 pm.
I've only been to YP once, and I really enjoyed it, but the location and their hours make it difficult for me to get over there on a regular basis. I've been wanting to try Carali's since it's closer to my home.
I'm not sure why YP's owner is unhappy about some competition. It's not like YP is the first Peruvian chicken joint in town (the long-gone Mr. Pollo gets that honor, I believe?). I think there is room in a city of this size for more than one restaurant of this kind. If anything competition tends to make people up their game (even though YP is totally on top of theirs right now).