Bring a large pot of water to boil. Add the chicken breasts for about 30 minutes or until it is completely cooked through. Drain water and allow the chicken to cool. When cooled, shred the chicken by hand or with 2 forks.
In a small bowl, mix together the heavy cream and cornmeal. Allow the mixture to sit while you prepare the rest of the chili.
Heat the butter in a large pot of medium heat. Add the bell peppers, onions, garlic, and jalapenos, allow the veggies to soften for about 8 - 10 minutes. Add the chicken, broth, green chile, beans, and chili powder and bring the soup to a rolling boil, lower the heat, cover and let simmer for 20 minutes.
Add the cornmeal and heavy cream mixture, and let simmer for another 10 minutes. Add the lime zest and juice, bring back to a simmer then turn off stove. Remove from heat and let stand for a few minutes to thicken.
Serve chili with cilantro and tortilla chips