In a large stock pot, heat the oil over medium-high. Add onions, 1/3 cup cilantro, and garlic. Saute 3 minutes.
Stir in chicken broth, tomatoes, whole raw chicken breasts, all the spices, and 3/4 teaspoon salt. Push the chicken breasts to the bottom of the pot. Bring to a boil.
Add the carrots. Return to a boil, then reduce the heat to medium and cook another 10-12 minutes.