Preheat the oven to 425 degrees F (218 degrees C). Pat the chicken very dry with paper towels, then brush both sides with olive oil.
In a small bowl, whisk together the baking powder, smoked paprika, garlic powder, dried oregano, salt, and pepper. Season the chicken on all sides with the spice mixture. Use your hands to pat the seasonings gently into the skin.
Arrange the chicken pieces on a large wire rack fitted over a large baking sheet, skin side down.
Bake chicken in the oven for 15 minutes, on the middle rack.
Flip the chicken pieces over, skin side up. Return to the oven and roast for 30-40 more minutes, until the skin starts to look a little crispy and the internal temperature reaches at least 170-180 degrees F (77-82 degrees C).
Place the pan 4-6 inches away from the broiler, and broil for 1-3 minutes to get the chicken extra crispy.
Let the baked chicken rest for 5 minutes before serving.
