Heat the oil in a 6-quart saucepot over medium-high heat. Add the chicken in 2 batches and cook for 10 minutes until it's well browned on both sides. Remove the chicken and set aside.
Add the pepper and onion to the saucepot and cook until the vegetables are tender-crisp.
Stir the soup, water, vinegar, brown sugar and chile pepper in the saucepot. Heat to a boil. Return the chicken to the saucepot. Reduce the heat to low. Cover and cook for 20 minutes or until the chicken is fork-tender.
Remove the chicken from the saucepot to a cutting board. Using 2 forks shred the chicken. Return the chicken to the saucepot.
Cook for 10 minutes or until the sauce is thickened.
Serve the chicken mixture on the buns. Top with the cheese, if desired.