standard fiberglass is too flammable and not approved for that application. You don't want to give the insurance company any cause for denying claims.
They make a special high temperature product that you can use around the front of a fireplace. Its safe over 1000 degrees. There are actually two varieties one is yellow, and a higher temp product is white. However, I would use firebrick like the other post specifies in the chimney. That is what is recommended & I would not deviate.