Hey NN,
I also live in Greenville (downtown), and we've been wanting chickens for a while. A neighbor told us that a man in the neighborhood used to have some chickens, but the city confiscated them, so we just took his word that chickens aren't allowed. (However, the man with the chicks also had a couple of really loud roosters.)
Don't know if you've found the answer yet, but I was thinking this afternoon and I looked at the city's website, and found I could look up the municipal codes through a link at
http://www.municode.com/resources/gateway.asp?sid=40&pid=13105
Here is what the law says:
Sec. 4-7. Keeping domestic fowl; no disturbance of others.
No person shall keep on premises located in the city any chickens, turkeys, ducks, guineas, geese, pheasants, pigeons or other domestic fowl, in quantities or in a manner as to unreasonably disrupt or disturb the peace and quiet of any person, or to interfere with the reasonable use of property or enjoyment of life by any person, or unreasonably to cause damage, destruction, detriment or impairment to public or private property or to the property's value, or to cause unreasonable annoyance or disturbance to any other person or to unreasonably cause offense to another person by reason of noise, odor, filth, vermin or other causes.
(Ord. No. 98-39, § 1, 6-8-98)
Sec. 4-8. Coops for containment of fowl.
No person shall confine fowl in coops or other enclosures less than 18 inches in height. The coops or other enclosures shall allow fowl to move around freely within the coops or enclosures. All coops or other enclosures used to confine fowl shall be provided at all times with clean food and pure water placed in containers outside of the coops or other enclosures, protected from contamination, and accessible to the fowl at all times. Coops or other enclosures used to confine fowl shall be provided with clean litter and cross-ventilation at all times.
(Ord. No. 98-39, § 1, 6-8-98)
So it appears that as long as your chickens aren't disturbing the neighbors or causing a stink (literally or figuratively), then chickens are legal in Greenville.
Hope this helps! I've just emailed my husband to tell him the good news, and I can't wait to get some chicks now!
A fellow Greenvillian and future chicken owner,
Jules C.