This is possible, but you need to adequately support the remaining chimney structure, and this will usually involve inserting some steelwork (i.e. RSJ) into the wall in your roofspace. There may be Building Officer involvement, especially if the chimney is on a party wall - I've had to repair a number of botched chimney removals and neighbours are always unhappy when their alcoves develop major cracks after next door has done something daft.
daveedo, March 2009