Can I attach drop ceiling molding to a brick chimney?
The answer to the code question is variable according to your location, especially if you're in the US as there will be federal, state, county, and maybe even city codes with which to comply. 

Besides codes there's simple common sense answers. I think I understand that the stove's pipe goes up an actual brick chimney, not just exposed through the ceiling, and my answer assumes that. I can't see any reason why you can't run the drop ceiling up to the chimney as long as you use fire-rated materials, that means the tracks, track fittings, and tiles themselves. You should make sure about that for the whole drop ceiling really.