Sometimes people do not like the appearance of a Class A chimney on the outside of their home. It is very common is to build a wooden chase around the factory built chimney. This way you can use whatever material you would like to finish off the chase. You can use cultured stone, stucco, siding or another suitable material that matches your home.
To finish off the top of the chase cover a stainless steel chase cover is needed with a storm collar. Every stainless steel chase cover is custom made. Call and order one from a reliable chimney supply company.
It is always a good idea to insulate the chase. Also, as always, make sure inside the chase you maintain your clearances to combustibles using the proper wall straps.