Preheat oven to 385 degrees F.
Brush an oven-safe baking dish with a light coating of olive oil in the bottom and all around the insides.
Rinse chicken breasts and pat dry. Place in the center of the baking dish.
Peel and slice potatoes into 1/4 inch rounds. Arrange the potatoes around the chicken breasts overlapping until the remainder of the dish is filled.
Drizzle olive oil over the potatoes. Salt generously and crack on some black pepper.
Pour in a splash of white wine just enough so there is some liquid in the bottom of the pan. You can substitute water for the wine if you prefer.
Coat everything with oregano. Be generous, really pile it on.
Cover baking dish with foil. Add a few small holes to vent.
Place in the oven and bake for 60 minutes. Check it halfway through to make sure it isn't drying out. Add some water if it needs it. You need liquid for the potatoes to cook properly.
Remove foil and bake for another 15 minutes uncovered. The chicken is done when you poke a knife in and the juices run clear.