Triple check is not legally possible in chess. However, double check is possible, although much less common than a single piece check. The only way that triple check can occur is via illegal moves, such as in beginner chess, where a King moves to a square attacked by 3 enemy pieces, or else the King is left in check and extra pieces move to attack it.
Related Chess Rules Topics
Read more about these related chess rules, chess puzzles, and other chess tactics and strategies: