I found a E. Chamberlain, 1850, percussion pistols at Southbridge, Massachusetts and a Joseph Chamberlain around 1815, general gunsmith in Albany, New York but no P Chamberlin & Co.
It was fairly common to change the spelling of names back in those days so there is a possibility that one or both of these somehow are tied to P Chamberlin & Co.
It's also possible that P. Chamberlin & Co was a hardware store or a gun dealer that bought and sold guns with his companies name stamped on them.
That was also pretty common.