Season the chicken generously with salt and pepper. Heat the olive oil in a large dutch oven or other heavy pot over medium-high heat until shimmering. Add the chicken skin-side down and cook until well browned and crisp, moving the pieces around as needed so they cook evenly, 5 to 7 minutes. Flip the chicken and cook on the other side until lightly browned, about 3 minutes.

Meanwhile, chop the onion and celery. Have the lemon, cut one half into quarters, then thinly slice the other half. Cut the potatoes into chunks.

When the chicken is finished browning, remove to a plate and add the onion, celery and garlic to the pot. Cook, stirring, until tender, 3 to 5 minutes. Add the sliced lemon and potatoes, stir and cook 30 seconds. Add the chicken broth, olives, bay leaves and ½ teaspoon salt. Bring to a boil, then add the chicken, skin-side up. Reduce the heat to low, cover and simmer until the chicken and potatoes are cooked through, about 20 minutes.

Meanwhile, chop the parsley. When the chicken is finished cooking, add the lemon juice to the pot and season with salt, discarding the bay leaves. Sprinkle with the parsley.