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1.
An old term from the Southwest that refers to a gun that is not worn daily. It won't have the scratches, wear marks, etc a daily wear gun would have. These guns were not something that were never used or "useless." In the time the term came about they were functional guns (sometimes, heavily modified for better accuracy/reliability/etc) that might have some custom engraving, polishing, or custom grips. They didn't make many guns purely for show - they made guns to use and users modified them for show. They were normally worn in tooled leather holsters as opposed to daily wear holsters - which were plain.

In the revolver days (before semi-auto pistols) a church gun was a normal firearm as described above. After the semi-auto pistols arrived on scene this term applied to mostly Colt 1911's. Current times this can apply to any firearm that has custom work designed to enhance mainly appearance and, much of the time - functionality.

However, this should not be confused with a (today's term) "bling gun" - which can imply that the gun is more for show than effectiveness. Or that the user is not proficient in its use because it is only worn on special occasions.

In the Southwest BBQ's could be at a casual get together, a special event, wedding, or a different/very formal affair.

Also known as a "Church gun," a "Court Gun," or "the 4th of July gun" (in Wyoming) for obvious reasons.
"I'm wearing my BBQ gun to the wedding."

"He's wearing his Sunday best and his BBQ gun."

"The Sheriff showed up to court wearing his BBQ gun."
by Shaneaus February 04, 2013
 
2.
The type of aesthetically pleasing or impressive-looking firearm that you might show off at a BBQ or on other social occasions, but may be less than useful.
John got a new Glock, but it's mostly going to be a BBQ gun. He doesn't know how to use or clean it.

Uh-oh, here's Mike with his BBQ gun again. Everyone act impressed.
by Kha December 15, 2007