I heat with gas. Should this chimney be cleaned?   

1. In most cases no, for cleaning and without a doubt at least have it inspected.
    
2. Although gas is generally a clean burning fuel, the chimney can become non functional from birds nests or debris blocking the flue.
    
3. Incomplete combustion of gas is relatively rare but can occur in some circumstances. Insufficient oxygen is one cause of improper combustion. Have your furnace inspected by a certified gas technician.