Welcome to the Forum, I would estimate between 1963 and 1965 for the age of your Mod 37. Value depends on condition. Without several good clear close up pictures there is no telling. The "book" shows ANIB as $650, and Fair as $250. Somewhere in the middle around $400. Alloy frames show wear easier than steel, so values aren't astronomical.
The number on the butt is the serial number (not the model number). Based on others near your serial number I guess the factory shipped your Chiefs Special in the summer of '68.
Yours appears to be in excellent condition, and you have the box (assuming the serial number on the box matches the gun) so I'd put it at the higher end of the scale, but it is mostly a matter of what a buyer is willing to pay. I don't see many Model 37s selling at the top of the scale.
Seeking Age and Value
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