Who was the very first one to ever use the quote "Chess is art"? Like who was the first one?
I don't think anybody has made such a claim. "Chess is an art" is another matter.
Vaclav Havel (former Czech prime minister) is supposed to have said that when he visited the Carlsbad tournament.
Karpov is supposed to have said "Chess is everything - art, science, and sport."
If anyone should know it would be Marcel Duchamp the artist who gave up art for chess. Although since he put forward a urinal as a work of art I would hope that he would put chess on a more elevated plane.
Perhaps the most quoted saying about the nature of chess is Tarrasch's
Chess, like love, like music, has the power to make men happy
which does it for me.
Apparently this is a quote attributed to Alexander Alekhine: "To me, chess is not a game; it is art." http://www.huffingtonpost.com/lubomir-kavalek/chess-art-under-alekhines_b_3195822.html
This is probably a translation from Russian (or maybe French?), so there also exists Brian Towers preferred version: "Chess for me is not a game, but an art. Yes, and I take upon myself all those responsibilities which an art imposes on its adherents. – Alexander Alekhine."