Sort of. A player can claim a draw if no pieces are captured and no pawn has been moved in the last fifty consecutive moves. I believe it has to be the 51st move and the pawns (or any other non-king piece) cannot move or the count will start over again.
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If we only left with a king....or have pawns which are being blocked....the opponent must checkmate us in under 50 moves or it will be called a draw?