USMCJS,
Nice rare gun! You have a Model of 1953 New J frame, Chief Special Target which started with a 4 screw side plate but yours is most likely a 3 screw w/that serial #. It's a 'pre model 36' as you said from the 1959 production run of 198 described below. The order for stamping frames with Model #s came down in 1957, but as always with S&W, there were many frames in production already that didn't get stamped. After a long transition period, all Smith's models eventually were stamped with their respective model #s.
Here's a brief history of all J frame target model production of BLUE Models 36, 37, 50, the earliest of them not model stamped:
Chiefs Special Targets were un-cataloged, sporadic production from 1955 thru 1990. The first regular production began in 1996 w/the Mod 60-10. Total production reported by SCSW is 2136 up thru 1978 and serial numbered in the Mod 36 serial range.
* 312 in 1954-55, Pre Model 37, 3 ½" barrel, reportedly but unconfirmed. These are not in the final count of 2136.
* First run of 100 in 1955, Pre Model 36, # range 55050-57919, 2" Sq butt, 2nd style flat latch, 4 screw frames, pre war style hammer.
* 14 in 1956, Pre model 36, 2nd style flat latch, some may have 4 screw frames.
* 198 in 1959, Model 36, # range 149811-150133, 2" Sq Butt, 2nd and 3rd style flat latch.
* Sporadic from 1965 – 1975, Mod 50, 2" and 3", Rd or Sq Butt, early w/3rd style flat latch and/or diamond grips, a few with 3" bbl, RR front, w/o rear sight and wide trigger.
* 1006 in 1966, Model 36, # 391773-392778, 2" Sq Butt. 3rd style Flat latch or standard TP with diamond grips.
* 568 made in 1973-1975, Mod 50, # 930j45-936j19, 2" Sq Butt, standard thumbpiece. 3 known in nickel that lettered as 36-1, SCSW p. 217, which appear to be left over from this Mod 50 production.
* 213 in 1975 (only 202 sold), Model 36-1 (-1 due to HB), # range 2j3134-2j3347 (actually 214 S/Ns), with a front sight base and pinned 3" HB (w/o barrel shroud), and Sq Butt. Appear to be the only Targets with ramp base front sight prior to the Mod 36-6s with full shroud. Special feature code on box label: G347.
* 37 in 1978, Mod 50, prefix # range 933j-936j, 2", Sq Butt. Unknown if they have front sight ramp base.
* 615 in 1989, Mod 36-6, 3" HB, front sight ramp base, full lug and Rd Butt, .340 combat trigger, black bead blasted, un-cataloged.
* 1991, Mod 36-8 with full-lug, limited edition; no more info known to me.