There are lots of souvenir shops downtown, like around Ford's Theatre or the one in the McPherson metro station, that are definitely locally owned. You can probably find either an officially licensed hat or a knockoff, either way zero chance it's actually made locally.

There's also the $5 hat outside the stadium on game day option.

Or just buy an official hat at the the team store, the Lerners' business empire is a local enterprise, just not "small." It's open during games and also 10-4 on non-game days.

I recommend the blue hat, the red hat is jinxed IMHO.