50-500 usd
Your Smith and Wesson model 37 chiefs special airweight will bring 450 dollars in new unfired condition.It may bring more if the buyer is really motivated.
45 years old
Made in 1953. Model Numbers did not come into use unitl @ 1957. Sounds like you have a Chief Special Airweight. Later numbered as a Model 37.
Someone modified it.
69-70
100-500 USD
$20
Up unitl @ 1957 model numbers were not used. Check inside the frame near the crane, it has a model number, it will be there.
Informaiton not available in the public domain.
50-450 USd
My serial # is near yours and I purchased it new in 1968.