I should have ask about the finish, but I am going to presume it was either blued or nickel plated. If not disregard this information, but by now you can see that posting
all of the details, not just the serial number, is very important.
I think you have a
Smith & Wesson Chief Special (pre-model 36). These were made between 1950 and 1999, within a serial number range running from 1 to 786,544. In 1957 the factory started stamping the model number (36) on the frame behind the yoke cut-out (the yoke in the part the cylinder swings out on). As your revolver is not stamped with a model number it was made before 1957, and I would roughly date it has having been made during the very early 50's.
Two other points that might narrow the date of manufacture:
If your revolver has a screw in the front of the frame, just above the front of the trigger guard, it was made before 1953
If your revolver lacks this screw, but has a large-headed screw on the right side of the frame at the top/rear near the rear sight, it was made between 1953 and 1955. This large-headed screw was deleated around serial number 75,000. All of the above dates are approximate.
If the stocks are original to the gun (very important to collectors) you will find the serial number marked inside one of the grip panels.
If you want to confirm all of the details, including the exact date the gun was shipped from the factory, and to what distributor or dealer; S&W will have their historian go back and research the original factory shipping records. You will thereafter receive an official letter from them. the fee is a reasonable $30.00, and you will find out more at the following link:
http://www.smith-wesson.com/webapp/...catalogId=11101&content=25301§ionId=10504