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No, there is not. First, stalemate is a specific condition that, by the rules of Chess, results in a draw. Stalemate is when the King is not in check and the player cannot make any legal move. In some Chess variants, such as Chinese Chess, stalemate is a win for the player who delivers it. But in Chess it is a draw for both players. Your question can more accurately be phrased by asking whether putting your opponent into check a specified number of times causes the game to end in a draw. Again, the answer is no. There is no rule to precisely this effect, but there is a rule that can cause the game to end in a draw due to repeated checks. This is the 3-times repetition rule: 'If the same position with the same player to move is repeated three times in the game, the player to move can claim a draw.' It is possible to use repeated checks to force the same position to repeat three times.