Place chicken in a medium saucepan; add water to cover. Bring to a boil. Reduce heat to medium, and cook, uncovered, 15 minutes or until chicken is done. Drain. Let chicken cool to touch. Chop chicken into bite-size pieces.
Combine chicken, bean sprouts, water chestnuts, and green onions. Combine vinegar, soy sauce, and oil; pour over chicken mixture, tossing gently.
Line each pita half with a lettuce leaf; spoon chicken mixture evenly into pita halves.