Wanna play a game of chess?

[Balin999]

I'm just reading the LotR for the 7th time now, for the 4th time in english. Yesterday i noticed this:

A pawn did Gandalf say? Perhaps; but on the wrong chessboard

Said to Beregond by Pippin.
Now I thought: How did the people of Middle-Earth ever get to the chess game?
Did they invent it? I don't think so. As far as i know, chess was invented in Asia and came to Europe in the, well let's say... 17th century (correct me if i'm wrong).
now that's quite the time in which the whole story of middle earth could be set. Meaning, the plot of Lord of the Rings.
So, the people of Middle-Earth could have gotten it from the west, from Valinor, by the people of Numenor, by the elves, something like that. (If they could invent the Palantiri, why shouldn't they invent chess?)
BUT, and now this sounds absolutely impossible to me, but what if one of the two missing Istari, or even both, that went to the East, learned it from the people who lived there, brought the game to western middle-earth, and then vanished again in the east.
There are reasons why this could be possible: The Istari were intellectuals, obviously.
Istari are rather curious in learning new things.
And, that's a guess, they love entertaining themselves while they are not busy with something.
So, chess would seem rather interesting to them. That doesn't give an explanation why they should go back to the west and bring it with them, but I gave it a try.
I know that this is rather ridiculous, nevertheless I appreciate any serious answer.