Code:
import tensorflow as tf
import numpy as np
import chess
import chess.pgn
import io

# Define the neural network architecture
model = tf.keras.Sequential([
    tf.keras.layers.Dense(256, activation='relu'),
    tf.keras.layers.Dense(256, activation='relu'),
    tf.keras.layers.Dense(len(chess.SQUARE_NAMES)*len(chess.SQUARE_NAMES), activation='softmax')
])
# Play chess games against itself and append moves to dataset
board = chess.Board()
self_play_games = []
while not board.is_game_over():
    input_ = np.zeros(len(chess.SQUARE_NAMES)*len(chess.SQUARE_NAMES))
    for move in board.legal_moves:
        input_[move.from_square*len(chess.SQUARE_NAMES)+move.to_square] = 1
    output_ = model.predict(np.array([input_]))[0]
    best_move_index = np.argmax(output_)
    best_move = chess.Move(best_move_index // len(chess.SQUARE_NAMES),
                           best_move_index % len(chess.SQUARE_NAMES))
    if board.parse_san(str(best_move)) in board.legal_moves:
        board.push(best_move)
        self_play_games.append(best_move)  # append move to self-play games
    else:
        print(f"Illegal move: {best_move}")
    print(board)

# Append self-play games to dataset
for game in self_play_games:
    board = chess.Board()
    dataset.append(game)
    for move in game:
        input_ = np.zeros(len(chess.SQUARE_NAMES)*len(chess.SQUARE_NAMES))
        input_[move.from_square*len(chess.SQUARE_NAMES)+move.to_square] = 1
        output_ = np.zeros(len(chess.SQUARE_NAMES)*len(chess.SQUARE_NAMES))
        if board.parse_san(str(move)) in board.legal_moves:
            board.push(move)
            legal_moves = list(board.legal_moves)
            if legal_moves:
                output_[legal_moves.index(move)] = 1
            else:
                print("No legal moves")
        else:
            print(f"Illegal move: {move}")
        inputs.append(input_)
        outputs.append(output_)

# Train the neural network on the updated dataset
inputs = np.array(inputs)
outputs = np.array(outputs)
model.compile(optimizer='adam', loss='categorical_crossentropy')
model.fit(inputs, outputs, epochs=10)

# Prepare the dataset of previously played chess games
dataset = []
for i in range(1000):
    board = chess.Board()
    game = []
    while not board.is_game_over():
        input_ = np.zeros(len(chess.SQUARE_NAMES)*len(chess.SQUARE_NAMES))
        for move in board.legal_moves:
            input_[move.from_square*len(chess.SQUARE_NAMES)+move.to_square] = 1
        output_ = model.predict(np.array([input_]))[0]
        best_move_index = np.argmax(output_)
        best_move = chess.Move(best_move_index // len(chess.SQUARE_NAMES),
                               best_move_index % len(chess.SQUARE_NAMES))
        if board.parse_san(str(best_move)) in board.legal_moves:
            board.push(best_move)
            game.append(best_move)
        else:
            print(f"Illegal move: {best_move}")
        print(board)
    dataset.append(game)

# Play chess games against itself
board = chess.Board()
while not board.is_game_over():
    input_ = np.zeros(len(chess.SQUARE_NAMES)*len(chess.SQUARE_NAMES))
    for move in board.legal_moves:
        input_[move.from_square*len(chess.SQUARE_NAMES)+move.to_square] = 1
    output_ = model.predict(np.array([input_]))[0]
    best_move_index = np.argmax(output_)
    best_move = chess.Move(best_move_index // len(chess.SQUARE_NAMES),
                           best_move_index % len(chess.SQUARE_NAMES))
    if board.parse_san(str(best_move)) in board.legal_moves:
        board.push(best_move)
    else:
        print(f"Illegal move: {best_move}")
    print(board)

Error:
1/1 [==============================] - 4s 4s/step
---------------------------------------------------------------------------
IllegalMoveError                          Traceback (most recent call last)
<ipython-input-7-f75f73836199> in <cell line: 16>()
     22     best_move = chess.Move(best_move_index // len(chess.SQUARE_NAMES),
     23                            best_move_index % len(chess.SQUARE_NAMES))
---> 24     if board.parse_san(str(best_move)) in board.legal_moves:
     25         board.push(best_move)
     26         self_play_games.append(best_move)  # append move to self-play games

1 frames
/usr/local/lib/python3.10/dist-packages/chess/__init__.py in find_move(self, from_square, to_square, promotion)
   2331         move = self._from_chess960(self.chess960, from_square, to_square, promotion)
   2332         if not self.is_legal(move):
-> 2333             raise IllegalMoveError(f"no matching legal move for {move.uci()} ({SQUARE_NAMES[from_square]} -> {SQUARE_NAMES[to_square]}) in {self.fen()}")
   2334 
   2335         return move

IllegalMoveError: no matching legal move for f3h2 (f3 -> h2) in rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1