Its a messy job but is often done. Obviously you work from the top down after removing (rerouting) all connected appliances. Access from the roof, attic and each floor. Avoid temptation to use the chimney as a debris chute, or you will have a dangerous brick avalanche when you open the smoke shelf or bottom. Chimney may consist of exterior brick veneer, supporting block and inner clay tile liner. You will have a lot of heavy debris. Note job entails roof repairs and closure of each ceiling/floor penetrated by the chimney.