Probably not the USA. There. I've eliminated one possibility.
which country invented chess

India , as Chaturanga. From there it was migrated to arab countries by merchants. From arab countries it was carried forward to europe.
Also from india to china by chinese scholars.

Wikipedia says modern rules since 1475, so Spain.
But En Passant and the initial Pawn double-advance didn't come up until very later, and not by Spaniards (I think) ... so we could say Chess is a transnational invention.

In the same spirit of I'm-too-lazy-to-use-Google, let me throw out some similar questions I wondered about:
Which came first: chess or shogi? Were they independent or did they influence each other?
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(p. 17)
Don't bother suggesting rule changes to chess. Everyone goes through this
phase, but try to resist it. One of the greatest pleasures of chess is that you can
replay games from long ago. And there is also the hope that today's games may
live on indefinitely. If we were to change the rules, we would interfere with this
sense of continuity. If you feel that you absolutely must share your brilliant new
idea with the chess world, keep in mind that the last changes date from the end of
the 15th century!
Eade, James. 1996. Chess For Dummies. Foster City, CA: IDG Books Worldwide, Inc.

Why would you assume chess was invented by a country? Maybe it was invented by people not connected to a specific country.

eskimos invented it
I can't tell if you're joking because very early chess pieces were found made from walrus tusk, which almost sounds like eskimos, except on the wrong continent:
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(p. 331)
Lewis chessmen Chess pieces made of walrus tusk discovered on the Isle of
Lewis (outer Hebrides) in 1831. They were probably made in the 11th or 12th
century and now are on display in the British Museum.
Eade, James. 1996. Chess For Dummies. Foster City, CA: IDG Books Worldwide, Inc.
wich did