Stopped by my local gun store and found this like new in the box Model 36 3" from 1969.
It had been in the last showcase since July and nobody was interested because it wasn't "tactical". Today is my day!

I hope you stopped on the way home and bought a lottery ticket.
That is a beauty! Congrats
Congrats.
Does it have a six-digit serial number or one that begins with a J?
Yes. J24XXX
Serial number 778528 - no J prefix. Any idea when it was built?
Just a shooter and my carry gun, some blue wear but right as rain otherwise.
S&W likely shipped it in 1969. The high serial number in those
early Chiefs series went to 786544 that year.
Does it have a round butt and magna stocks like the OP's?