Place chicken breasts in a shallow pan so that they don't overlap with one another. Add enough water to just cover the chicken and turn the heat to medium. Once the water starts to boil, turn off the heat. Flip the chicken breasts to the other side and cover the pan tightly for 10 minutes or so. Check to make sure they are cooked fully and remove the chicken from the pan. Shred the chicken breasts.
In a separate pan (one that's large enough for chili), bring 3 cups of chicken broth to a low boil. Add chicken, salsa, beans, and corn. Stirring constantly, add the cheese. Wait until the cheese melts before correcting the flavors.