1. In processor, chop chiles. Spoon into small bowl. Add 2 tablespoons olive oil, lime juice, salt and pepper.
2. In glass baking dish, coat chicken with chile mixture. Cover; refrigerate for 1-1/2 to 2 hours to marinate.
3. In large pot, simmer, uncovered, broth, garlic, onion, half the tomatoes and 1 sprig mint for 30 minutes, until reduced to about 2 quarts. Strain; return broth to pot.
4. Prepare grill with hot coals, or heat gas grill to hot (Oven Method below). Arrange coals around outside of grill. Brush rack with vegetable oil. Place chicken in center of grill, not over direct heat. Cover; cook 25 minutes or until internal temperature is 180 degrees F. During last 5 minutes, brush corn with 1 teaspoon olive oil. Grill over heat, turning, 5 minutes.
5. Bring broth to a boil. Add carrots, potatoes and remaining tomatoes; simmer 15 minutes, until tender.
6. Remove kernels from cobs. Divide broth and vegetables among 4 large bowls. Place 2 pieces of chicken in each bowl. Sprinkle corn over each bowl and garnish with the remaining mint. Squeeze lime over each serving.Oven Method:
7. Bake marinated chicken at 450 degrees F for 40 to 45 minutes.