Mix allspice, cumin and thyme in small bowl. Reserve ¼ teaspoon for the salsa. Mix ¼ cup of the orange juice, 1 tablespoon of the oil, salt and remaining spice mixture in large resealable plastic bag or glass dish. Add chicken; turn to coat well. Refrigerate 15 minutes.
Meanwhile for the salsa, mix avocado, mango, remaining 2 tablespoons orange juice, 1 tablespoon oil and reserved spice mixture in medium bowl. Cover. Refrigerate until ready to serve.
Remove chicken from marinade. Discard any remaining marinade. Grill chicken over medium-high heat 4 to 6 minutes per side or until cooked through. Cut chicken into thin strips and serve in warmed tortillas topped with the avocado and mango salsa.
