Marinate chicken in vinaigrette, covered, in refrigerator for at least 4 hours or overnight. In a small bowl, combine the sauce ingredients; chill until serving., Drain and discard marinade. If grilling the chicken, lightly oil the grill rack. Grill chicken, covered, over medium heat or broil 4 in. from the heat until a thermometer reads 170°, 4-7 minutes on each side., Cut chicken into strips. Fill each pita half with chicken, cucumber, tomatoes, onion and cheese; drizzle with sauce.