It's not Snap-on, as I have the same box from Craftsman, with the crown logo. It was made by, as Rileysan says, AMD/Remline. The question I have, does the outside look painted by hand, or is the black seemingly the original color? If it looks painted, I would guess either PowrKraft or sold as a Remline.
By the way, my dad lived in Lodi as a little kid after the war, when the town was still very much a German-speaking town. My great grandmother ran a boarding house.
EDIT: I just went and looked at my Remline top box, and it has a square logo and little men on the drawer pulls. Also, the body is grey while the drawers, inside and out, are red. My Craftsman, top and bottom boxes, are grey everywhere, with just simple decorations on the pulls. If you go through the rest of this thread, you will find a PowrKraft set to check the pulls on. Don't know if that helps, but it is what I got.