Heat gas or charcoal grill. Between pieces of plastic wrap or waxed paper, place each chicken breast smooth side down; gently pound with flat side of meat mallet or rolling pin until about 1/4 inch thick. Brush all sides of chicken with oil. In small bowl, mix grill seasoning, brown sugar and chili pepper powder; sprinkle on both sides of chicken.
Place chicken on grill over medium heat. Cover grill; cook 5 to 6 minutes, turning once, until chicken is no longer pink in center.
Meanwhile, in small bowl, beat remaining ingredients with wire whisk until blended. Drizzle mayonnaise mixture on 4 serving plates. Top with chicken.