Question: can a king move without check in chess

Answer: Yes, A king can move one square in any direction (horizontally, vertically, or diagonally) unless the square is already occupied by a friendly piece or the move would place the king in check. As a result, the opposing kings may never occupy adjacent squares (see opposition), but the king can give discovered check by unmasking a bishop, rook, or queen. The king is also involved in the special move of castling.