In a large pot, saute the onion and red pepper in the olive oil over medium heat until the vegetables begin to soften (about 5 minutes).
Add the chicken broth and chicken breasts to the pot. Cover the pot and bring to a boil. Reduce the heat to medium low to simmer, and cook, covered, for 10 minutes. After the 10 minutes of simmering, check the chicken with a meat thermometer to make sure that it’s reached a temperature of 165 degrees. Remove the chicken from the pot and shred it with a fork (or use a mixer).
Return the shredded chicken to the pot. Add the corn kernels, black beans, salsa, salt, chili powder, and cumin. Stir the soup, then cover the pot and simmer over medium low heat for 10 minutes. Taste the soup and add additional salt or seasonings as desired.
Serve warm, topped with cilantro, jalapeno, lime, sour cream, cheese, avocado, or any of your favorite southwestern toppings.