Dig a hole about 1 foot into the ground. Place a layer of hot coals on the bottom, and cover with a 1/2 inch layer of dirt.
Rub the chicken breasts with oil, then season with garlic salt, pepper, and oregano. Wrap each breast securely in aluminum foil and place into the hole.
Cover the hole with about 6 inches of dirt and allow the chicken to cook for 3 to 4 hours. About 45 minutes before you are ready to eat, wrap the potatoes individually in aluminum foil, and place them in the coals of a campfire to cook. When the potatoes are ready, dig up the chicken and serve with potatoes.