Researcher Bart Nunnelly has reported of a couple of cases of hyenas in Kentucky. One was near Uniontown, and the other was spotted (no pun intended) near Lexington in 2004:
"About 10 feet in front of the car, on the grassy area next to the expressway, we saw a strange 'creature'. It looked like a hyena, bluish-gray fur with blackish spots or splotches. It was crouched down as if going to pounce. As our car passed it looked over at us. It's face had a snout and long teeth. It bared its teeth at us and we were so shocked we just drove on. I can't imagine what it was. It was about 3 feet tall at the shoulder with a sloping back and narrower haunches. Its head was big and it had a fur 'fringe' along its back."
I'm not sure why they say "I can't imagine what it was" if they just got through saying it looked like a hyena, but okay. And that's a lot of detail given from someone who saw it from a moving car.
We do know there are coyotes in Kentucky, and that sounds more believable than a hyena. Seen from a distance in a moving car, a dirty or splotchy-looking coyote could fit the description and be mistaken for a hyena, I suppose. See coyote photo below:
Two 2009 posts to Jeff and Claudia's blog speculate on wolf sightings. Wolves are increasingly common again in Kentucky, and have even been deliberately reintroduced in some areas. These, too, could easily be responsible for alleged hyena sightings. See Red Wolf and Gray Wolf photo below:
On the other hand, it's still not impossible that hyenas could have somehow entered Kentucky's environment, as escapees from zoos or private breeders. Stranger things have happened, after all, like the spate of kangaroo sightings in Kentucky in the 1970s.