2Mix thyme, red pepper, salt and allspice; rub on chicken with the back of a spoon.
3Cover 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.
4Cut chicken into 1/2 inch strips. Toss salad greens and dressing. Carefully toss salad mixture with grilled vegetables and papaya.