The 2nd Amendment. It goes back to the local militias who fought off the British in the Revolutionary War.
Of course, the 2nd Amendment applied to "well-regulated militias" for firearm ownership, and they had flintlocks and muskets instead of the automatic weapons of today.
Historically, settlers used firearms in frontier regions to hunt, so firearms were a part of life for a long time. Which lead to prolific ownership of guns for many Americans.
The Supreme Court case Distict of Columbia v Heller held that 2nd Amendment rights are not contingent upon association with any militia, and United States v Miller found that those rights apply to any weapon "in common use at the time", ie those in common use for lawful purposes, or those that would be used by a militia.
There was also
this report from a Senate committee in 1982 (Chaired by Orrin Hatch; link goes to a .PDF), which to my knowledge was the first time the "as a militia is necessary for the common defense" clause of the 2nd Amendment was
not seen as the defining characteristic of the rights granted by that Amendment. The 1939 Miller case indicated that a sawed-off shotgun was not a weapon inconsistent with what a militia might be allowed to carry, but still pointed to the "militia" clause in its decision.