Heat goals or gas grill. Mix thyme, red pepper, salt and allspice; rub on chicken witht he back of a spoon.
Cover and grill chicken 5 to 6 inches from medium heat 15 to 20 minutes, turning once, until juice of chicken is no longer pink when centers of thickest pieces are cut. After 5 minutes, add onions and bell peppers, turning 2 or 3 times, until crisp-tender.
Cut chicken into 1/2 inch strips. Toss salad greens and dressing. Carefully toss salad mixture with grilled vegetables and papaya. Serve salad mixture with chicken. Makes 4 servings.
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