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I have a Model 36, serial number 733XXX
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it just starts with 733, but no letters in the front.
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The first J-frame Chiefs Special, s/n 1, was made October 24, 1950.
In 1957 S&W began using model numbers. The Chiefs Special was assigned number 36 at s/n 125000.
The serial numbers reached 786544 in 1969. As the Gun Control Act of 1968 was just coming into effect S&W began a new serial number series with a "J" prefix.
Since yours has no prefix it was likely made in the late 1960s, most likely 1968.