Get out a large pot, put the oil in, and heat it up. Drop the chicken pieces in the hot oil and cook, stirring so they don't stick, until they are browned. This'll take about 6 minutes. Then sprinkle the chicken with the chili powder, cumin, and cayenne pepper.
Add the onion and bell peppers to the pot. Also 3 cups of water. Bring the whole deal to a boil, then turn the heat down slightly and simmer vigorously for 10 minutes, or until the liquid is reduced by 1/2.
Pour in the black beans, corn, remaining water, and tomato paste. Bring to a boil, then simmer on low for 30 minutes to thicken. Add salt and hot sauce to taste and serve.