Season chicken breasts with salt and pepper. In a Dutch oven or large soup pot, heat 1 tablespoon of olive oil. Saute chicken until cooked through. Remove from pot, chop into cubes, and set aside.
In the same pot, heat another tablespoon of olive oil. Add peppers, carrots, green onions, and garlic. Season with salt and pepper. Cook until soft for about 6-8 minutes.
Add chicken broth and bring to a boil. Turn down to simmer. Add ramen noodles and cook according to package, until tender, for about 2-3 minutes. Stir in cooked chicken, cilantro, and lime juice. Simmer until heated through. Serve in a bowl with lime wedges.
