Welcome to the forum. I have a later version of your Dad's gun and mine is marked as a Model 36. I can see why your Dad carried it. I own more than a few handguns and some vintage Smiths among them. My Model 36 is probably one of my most favored 38s and I carry it CCW quite often.

Sorry to hear about your Dad but I'm sure that he is very happy that you now have it and cherish it. My Dad has been gone now for 22 years and while he wasn't a "pistol guy" I have a rifle that was his that I cherish greatly. Each time you handle that Chiefs Special, you'll think of him. A nice heirloom to have and to pass on.