As I understand it from reading CH municipal code, you can open carry in most of Chapel Hill (per their own ordinances -- specifically CH Municipal Code Chapter 11, Article XIV) as long as 1) you've not been drinking or doing drugs; 2) you're not at a polling place or public assembly; 3) it's a firearm with a grip whose OAL is more than 6" in length ... or a gripless firearm whose OAL is more than 8" in length; and 4) it's not a weapon of mass death and destruction as defined in Chapel Hill statues (which are basically a) semi-autos or any kind with 20rnd capacity detachable magazine or larger [if you have such mag, whether or not the mag is in the so-called weapon of mass death and destruction] and b) semi-auto shotties with 6rnd capacity or more. The foregoing obviously presumes the area is not a lawfully posted no-carry zone or a place where carry is legitimately prohibited by other state or federal law.
Interestingly, CH municipal code excludes weapons of mass death and destruction as defined in NCGS 14-288.8 from its own definition -- probably to avoid any appearance of stepping on the NC general statute's terms.
I pay close attention to the above because the OAL of my EDC (a single-stack Walther PPS Classic) is 6.32".