Chimney does indeed appear to be slang for a black eye. In Northern Ireland. Urban dictionary has some very different ideas about what a chimney is slang for. All online connections to the song appear to be reasonably recent.
The song was made by Italian house producers who may or may not have been familiar with Ulster Slang. While the tune relied heavily or the Jackson 5, the words, if not the actual vocals, were lifted from Urban Discharge's song, Drop a House. The chorus of which goes "wanna drop a house on that B...." This imagery is more like wizard of oz where famously a house is dropped on the witch.
Unfortunately, I was unable to find out which was the original mix of drop a house. Some versions have the chimney line in and some don't. Possibly the line was taken from the tamperer song and added back in to the original.
Either way, sometimes a chimney is just a chimney.