ORIGINAL: Pavomesa
Depends what you're talking about. Rimfire? Pinfire? Paper?
I think about theoldest COMPLETELY SELF-CONTAINED round made in the U.S. is the S&W "rocket ball" made for the Volcanic pistol, the mechanism of which, modified of course, became the Henry then Winchester repeating rifles. The "rocket ball" was a hollow-based bullet with a charge of fulminate of mercury opriming compound in the hollow. The fulminate was both priming and propellant.
I think the "BB-cap", or "ball-cap"type round was originated in France as a 6mm indoor target round by Flobert and perhaps others as well, about 1847. (A lot happened that year in Paris!) It consisted (and still does, as the .22 BB Cap) of a round ball in a copper case propelled by fulminate alone. The .22 CB cap round is similar, but used a conical ball instead of a round ball.
The first commercially successful U.S.-designedcomplete round holding priming, powder, and bullet in acartridge case was the .22 Short, adesigned by Smith & Wesson foruse in the S&W No. 1 revolver. Some pinfire shotshells were made here also, but I am not certain when their U.S. manufacture began.