Old, but I guess for future reference..
Chillie's is owned by the DeAngelo's- Sicilian descent as well. Not sure of any Italians in Greenville that are not rooted there.
If it makes a difference, the people running Coby's now are Sicialian, too- or at least the family he married into is.
Chillies is one of the larger liquor stores in the state, so they'll have more of a selection, but you can't really go wrong either way.