Preheat the oven to 400 degrees Fahrenheit. Pat the chicken dry with a paper towel.
Put the chicken in a roasting pan, baking dish, or on a sturdy sheet tray. Add the potatoes to the pan surrounding the chicken.
Add the olive oil, lemon juice, lemon zest, oregano, salt, and pepper to a bowl and stir well to combine.
Halve a head of garlic and add to the pan. Brush the lemon and oregano mixture all over the chicken and potatoes. Brush the cut side of the garlic with olive oil and sprinkle with salt.
Roast the chicken for 30 minutes. Remove it from the oven. Remove the garlic and potatoes from the pan. Spoon the pan juices over the chicken. Depending on the size of the chicken, it may be done. If so, remove the chicken from the oven and set on a cutting board to rest.
If not done, return the chicken to the oven and let cook for an additional 15 to 30 minutes, or until an instant-read thermometer inserted into the thickest part of the chicken thigh shows an internal temperature of 165 degrees Fahrenheit.
Let the chicken rest for about 10 minutes. Taste for seasoning, then carve and serve!