The U.S. Constitution does indeed protect that right, however, there are people in positions of authority in the U.S. that would love the U.N. to monitor American firearm sales/ownership, and who believe civilian firearms should be "illicit."
McDonald v. Chicago
District of Columbia v. Heller
Proposition H: "restrict handgun possession among San Francisco residents within city limits to police and certain security professionals, and to ban the manufacture, distribution, sale and transfer of firearms and ammunition within the city."