Howdy Paul, and welcome aboard from ol' Wyo.
I'll be back to edit this in a minute or two with some details for you.
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When you roll the cylinder out, do you see a "MOD-37" stamp on
the frame in the yoke cut? Serial numbers in the database bracket
yours, and they are all Model 37s--Chiefs Special Airweights--in
.38 S&W Special caliber (the right side of your barrel might be
stamped "AIRWEIGHT" above "38 SPL. CTG.)"
What's the barrel length--2" or 3"? And does your Chiefs Special
have a round or square butt? I'm guessing it is blue, not nickel.