Light about 24 charcoal briquets. Wipe olive oil throughout the Dutch oven.
When the coals are really hot, put the Dutch on top of all the coals and let it get hot.
Throw in boneless, fat-trimmed chicken breasts in and let them brown.
After browning, remove the Dutch from the coals and put slices of red onion and red bell pepper on each of the pieces of chicken. Cover the pieces with your favorite barbecue sauce. Add some water for steam.
Split the coals. Put the Dutch on top of eight coals and put 16 coals on top. Let it bake for about an hour.
Keep checking to make sure there's enough water in the Dutch to steam the chicken but not too much to dilute the sauce too much. Also check the coals. If the meat is cooking too fast or burning, remove some of the coals to adjust the heat.
After the meat is done, put a slice of your favorite cheese on top of each chicken breast. I used Swiss.