Date: Signed 1792
The Buttonwood Agreement is the precursor to the New York Stock Exchange. It was signed in 1792 under a Buttonwood tree on Wall St.—hence the name. Lucky it wasn't a Monkey Puzzle Tree—that would not be a dignified name at all.
The agreement itself is fairly simple—24 local merchants agreed that they would trade only with one another, and that they would take a 0.25% commission on whatever they traded.
And in case you're thinking 1792 is too early for there to be stocks to trade, it wasn't—the first war bonds were released by Alexander Hamilton, in 1790, two years before, so you're wrong, and should probably keep your opinion to yourself.