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No, chess is a game of complete information as all moves that are possible and all variables are at hand at every move. You just don't know what your are talking about.
Just to play Devil's advocate, you're right in principle but there are some tiny bits of imperfect information in Chess. You can't assess some positions without knowing history of past moves.
For example,
* Black to play
* Black has a pawn in f4
* White has a pawn in g4
In that example it matters if White's previous move was g4 and it would allow Black to take "en passant" in g3.
There are some much rarer cases where it looks like one side can castle but it turns out they already did before and somehow the pieces ended up in castling position later in the game. You need to know if that side has castled already to know the full game state and available moves.
Of course those are very easy to handle for chess engines and are not enough to re-qualify Chess as a game of imperfect information.