Step 1

Heat the oven to 475°F with a rack in the middle position. In a large bowl, stir together the oregano, pepper flakes, 1½ teaspoons salt and ½ teaspoon black pepper. Sprinkle 2 teaspoons of the mix onto all sides of the chicken. To the remaining seasoning mix in the bowl, add the oil, potatoes, lemon halves and garlic, then toss to coat.

Step 2

Place the garlic in the center of a rimmed baking sheet, then arrange the chicken, skin up, around the garlic; this placement helps prevent the garlic from scorching during roasting. Arrange the lemons, cut sides up, and the potatoes in an even layer around the chicken. Roast until the thickest part of the breasts (if using) reaches 160°F and the thickest part of the largest thigh (if using) reaches 175°F, about 30 minutes.

Step 3

Using tongs, transfer the chicken and lemon halves to a serving platter. Push the potatoes to the edge of the baking sheet, leaving the garlic in the center. Using a fork, mash the garlic to a rough paste. Add the olives, capers and 2 tablespoons of the dill to the baking sheet, then, using a wide metal spatula, stir and toss the ingredients, scraping up any browned bits.

Step 4

Transfer the potato mixture to the platter, placing it around the chicken. Sprinkle with the remaining 1 tablespoon dill.