Place the chicken breasts, skin side up, on a small baking sheet. With your fingers, loosen the skin from the meat, leaving one side attached.
Cut thick slices of herbed goat cheese and place slices, topped with fresh basil under the skin of each chicken breast. The cheese will crumble a bit, but don't worry, it will be delicious!
Add the oil, garlic, and oregano to a small bowl. Zest and juice the lemon directly into the bowl and stir to combine. Generously brush each breast with the mixture and season with salt and pepper.
Bake the breasts for 35 to 40 minutes, or until cooked through. Chicken is cooked through when it reaches 165 degrees F when an instant read thermometer is inserted into the thickest part of the breast meat (be sure it isn't touching the bone).
Notes
To Store: Refrigerate chicken breast in an airtight storage container for up to 3 days.
To Reheat: Reheat leftovers in a 350 degree F oven until warmed through or warmed gently in the microwave.
To Freeze: For longer storage, freeze chicken in an airtight freezer-safe container for up to 3 months. Let it thaw overnight in the refrigerator before reheating.