In a large cast iron skillet melt 1 tablespoon of butter with 1 tablespoon of olive oil over medium heat. Add the garlic and stir in for a few seconds then add the potatoes. Stir until the potatoes are nicely coated with oil, butter and garlic.
Spread potatoes into a single layer. Cover and cook for 10-12 minutes stirring once during this cooking time.
Chicken
While the potatoes are cooking season both sides of the chicken with salt, pepper, and thyme.
After the potatoes have browned push to one side and add the remaining 1 tablespoon olive oil and 1 tablespoon butter to the free side. Add the chicken breasts to the pan. Cook, uncovered for 5 minutes.
Flip chicken and top with lemon slices. Cover and cook for about 10 minutes or until chicken juices run clear. (internal temperature of 170°)
Serve
Serve the potatoes and chicken along with your favorite vegetable or a side salad for a complete meal.
Notes
If you choose you can add vegetables like beans, carrots, or broccoli to the pan when you add the chicken. After you remove the chicken and potatoes from the pan you can also deglaze the caramelized drippings from the bottom of the skillet with a little white wine or chicken broth to make a light gravy.My cast iron skillet didn't come with a cover but I happen to have one from my pots and pan set that fits. If you don't have a good cover for your cast iron skillet, you can use aluminum foil to cover your pan.