We have very few dangerous animals in our area. The most dangerous animals in Chatham County are actually spiders and reptiles. Those are Black Widow Spiders, Brown Recluse Spiders, Copperhead Snakes and Cottonmouth snakes. The snakes are rare and most often bite dogs.
In Chatham County, fox, skunks, groundhogs and beavers are the most common animals affected by rabies. There have indeed been rabid beaver attacks in Pittsboro. Of course, unvaccinated domestic animals such as cats & dogs can get rabies if bitten by another rabid animal as well.
Generally speaking, raccoons, fox and skunks are nocturnal animals. If you see one of these animals out and about in the daylight hours, be careful around them as they could be rabid.
This said, most people never encounter a rabid animal in Chatham County.
You can also read more here about black bears in Chatham County.