Preheat oven to 400F. Wash the potatoes, then slice into strips (like I did) or quarter them. If using a medium potato, slice in half. Then slice each half into 3 or 4 strips.
Add the potatoes and chicken to a large ziplock bag or large bowl.
Prepare the sauce by melting the butter over low heat in a small sauce pan. Add the olive oil, butter, lemon Juice, Worcheshire Sauce, minced garlic, and the rest of the spices/seasonings. Stir to combine. (Optional step, but recommended: Raise the heat to medium-high and bring "just to a boil.") Remove from heat and let cool for about 5 minutes.
After the seasoning sauce has cooled off for about 5 minutes, carefully add it to the chicken and potato mixture. Toss to thoroughly coat the chicken and potatoes
Remove chicken and potatoes from the bag, or bowl, and place on a rimmed baking sheet. Drizzle any remaining seasoning mixture over the chicken and potatoes. Bake for 15 minutes. Toss or turn the potatoes to ensure even doneness. Bake for another 10-15 minutes or until the chicken is no longer pink and the potatoes are tender. Be careful not to overcook the chicken or it'll be dry. Thicker breasts will require a little more time than thin ones and vice versa.