Prepare a hot grill.
Combine the olive oil, chicken and spices in a shallow pan. Mix thoroughly so that the chicken is well covered with spices.
Peel and remove the seeds of the papaya. Cut the papaya into 2-inch rectangles. Pour the lime juice on the papaya and place on 4 separate skewers.
Cut the limes in half.
Place the prepared chicken breasts on the grill along with the papaya skewers and lime halves.
Cook the chicken 6 minutes each side, turning frequently. Turn the papaya skewers until the all sides are a light brown, about 10 minutes. After 4 minutes, squeeze the cooked limes onto the papaya skewers.
Nutritional information per serving: 290 calories, 18 g fat, 3 g saturated fat, 65 mg cholesterol, 70 mg sodium, 12 g carbohydrates, 2 g fiber, 23 g protein.