I think The House of Staunton located in Alabama may have what you're looking for. They have a website.
Where are the Ameriacn made chess sets?

I believe that all of the HoS sets are made in India. Nowhere on their site do they say "Made in USA".

@Capablanca: Pretty sure all the HOS sets are made in India.
EDIT: Day late and a dollar short again...

I thought I had read or heard years ago that they make them on site in Alabama. You could call or email them and ask.

There is a nice instructional wooden set made in Vermont, but it's not a Staunton design and it's not tournament size.

Unless I'm mistaken, all the tournament size wooden Staunton sets sold by House of Staunton, Mark of Westminster, and Jaques of London are all made in India.
I have four different wooden sets made by Chopra in India, each sold with the Mark of Westminster label. The sets are all well made and have my recommendation. The only problem I see is that the chessmen makers in India and their quality products should not need to hide behind an pretentious Anglo Saxon name.
I think ChessUSA & others use these names as a maketing ploy. Which sounds better " chess set number 10 " or " Capablanca Gambit set " ?

I received an answer saying they aren't made in the USA, that they are made in various locations overseas.

I received an answer saying they aren't made in the USA, that they are made in various locations overseas.
they usually avoid being explicit about country of origin and refer to nebulous "various locations overseas" based on the fact that they import boards from Spain, and I believe some of the theme sets come from England etc. But all their wooden turned sets are being manufactured in India.

which doesn't bother me. Lots of highly skilled artisans in Amritsar, and HOS handles quality control (or at least they used to under Frank's ownership).

Quality control is very important. Over the past three decades I have bought many different sets from YourMove/ChessUSA, and only one set had a defect: a crack in the base of a wooden queen.
Customer service is also important. That cracked queen was immediately replaced without question. I assume that all other respectable retailers have the same policy.
I think the HOS quality control used to be better, but my experience with their customer service "back in the day" was having to argue back and forth for many emails to get them to replace broken pieces until I was finally emailing Frank and then it was taken care of. I haven't gotten anything from them for many years as at least a while there it was simply paying much more for the same thing you could get on eBay from the manufacturers for less, but it seems like the prices have mostly evened out there... I just haven't had any need for another modern mass produced Indian set. The one I have is still in good condition and I don't really need another.

To get top-notch Q/A and C/S, it's probably best not to go with a retailer who offers little else besides a low price. The cost of a better product and service will always be reflected in what you pay.
I think Chess USA is the best retailer out there when it comes to fixing a problem. They replaced a broken piece for me in the past without a problem. Also the USCF has sent me a new piece that was damaged without question.

Everything coming out of India is mass-produced on multi axis lathes. There is hardly anybody anywhere in the world making chess pieces totally by hand anymore, but I do. I will replace missing pieces from sets as well. I use old-fashioned bench chisels. My knights are one piece, not two, unlike even the anitque Jacques sets. Its always been cheaper, easy, and more suited to mass production to make knights in two pieces. Mine are one-piece a carved turning, I don't take short cuts.
For several years I teamed up with Andy Summerville, also from the USA who makes the best chessboards you will ever find to make a truly unique chess set of outstanding quality with everything being handcrafted in the USA with woods from the USA by poeple from the USA. I'll make whatever design you want, but I specialize in replicating the original 1849 Staunton design, and a better 1849 reproduction set you won't find anywhere especially not overseas.

All my sets are massively weighted and come with four queens. Leather or felt pads. Made with American black walnut and Pearwood (a very traditional chees piece wood). I make sets to USCF specs for a 2", 2.25", 2.5" and 1.75" board square although i prefer a pawn with a wider base for each of those. I'll make or repair or replace whatever style piece you're mssing from your set.
After a considerable search, I have been unable to find a single Ameriacan made tournament size wooden Staunton chess set. The best I could locate was one with a half size king (2 inches).