That looks like it was a pretty high end fowler at one time.
Blackmore lists:
William 1 Merchant Birmingham, 1777-80. Became Chance & Homer (q.v.), then William Chance & Sons, 1812 - 21. Sold guns marked 'London'.
William 2 Son of William (1)? America merchants, 2 Coleman St. Bldgs., London, 1829 - 35. At same address became William Chance & Sons, 1836 - 42; William Chance Son & Co., 1843 - 56; William Chance & Co., 1858 Main premises at 152 Great Charles St., Birmingham, but guns marked 'London". As importers of hardware and firearms had branch in New York, 1842 -53 (Dir). Supplied American Fur Co. with 'Chiefs and North West' guns, 1835 - 45. (Parsons).
The second William was seems to be the most likely candidate.
George