Preheat the oven to 400 degrees F.
Arrange the potatoes, chicken, thyme, onions, peppers, 1 teaspoon salt and 1/2 teaspoon pepper in a wide, shallow roasting pan. Halve the lemon, squeeze the juice over top, and add the squeezed lemon halves to the pan. Pour the oil from the jar of artichokes into the pan, reserving the artichokes. Toss the chicken and vegetables together so that everything is nicely coated in the oil. Roast for 30 minutes.
Remove the pan from the oven and add the reserved artichokes, olives and anchovies, if using. Toss well to combine. Return the pan to the oven and roast until the chicken skin is crisp and golden brown, 15 to 20 minutes. If you find that the chicken skin is not crisping, broil on high for a few minutes to finish.
Serve family-style with some crusty bread to soak up all the delicious juices.