Heat oil in a large heavy skillet over medium-high heat. One at a time, slip a tortilla into the hot oil. If the tortilla starts to puff up, press it down with a fork. When crisp and brown, remove to paper towels. Repeat with remaining tortillas.
Place the chicken in a bowl, and separate with a fork. Stir in the mayonnaise. Dice the jalapenos (reserving the liquid), and stir them into chicken salad. Pour in 1 tablespoon jalapeno juice, season with salt and pepper, and stir well. To serve, spread the chicken salad on the tostadas.
