I know this is not exactly what you're looking for...sorry but at least it's a store that sells goat and isn't too far from Oak Brook.
There's a strip mall on Lake in Addison right where Army Trail Road ends. They advertise goat meat. Maybe I'm just taken in by the store name....the place is a little dingy but serves a broad ethnic community. It's in the strip mall that used to house Caputo's
Farm Meat Market
232 W Lake St
Addison, IL 60101
(630) 543-2122