It is interesting how the Baby Chief features carried over after the change to the larger grip frame and triggerguard were implemented. I recently purchased a Baby Chief serial number 34554 with all the early features. The serial number is close to one that shipped in June 1953 and while I know that S&W didn't ship in serial number order, I would think that mine shipped somewhere around that time.
It is a five screw gun with the serial number stamped on the barrel, cylinder and stocks as well as on the frame. It was sent back to S&W in the early seventies for a refinish and has the rework date of 11.73 on the grip frame along with a boxed R-S. Looking at the recoil shield, it doesn't appear to have been fired since it came back from S&W.
Unfortunately, due to poor storage, there was some rust spots on the frame and cylinder.