Heat gas or charcoal grill. In small bowl, mix sauce ingredients; set aside. (Sauce may become watery if it stands longer than 30 minutes.)
In another small bowl, mix lemon juice, oil and oregano. Brush lemon mixture over chicken, coating all sides. If desired, sprinkle with salt and pepper.
Place chicken on grill over medium heat. Cover grill; cook 15 to 20 minutes, turning once, until juice of chicken is clear when center of thickest part is cut (170°F). Wrap pita halves in foil; place on grill 1 to 2 minutes or until warm.
Place chicken, tomato and onion inside pita pockets. Top with sauce, or serve sauce on the side for dipping.