Season the chicken with 1/2 teaspoon salt and a few grinds of pepper. Heat a large Dutch oven or pot over high heat and add the olive oil. Add the chicken, skin-side down, and cook until golden, 3 to 4 minutes per side. Remove to a plate and set aside.
Reduce the heat to medium high. Add the garlic and cook 1 minute. Stir in the onion, carrots, tomato paste, sage and rosemary. Cook, scraping up any browned bits from the bottom of the pot, until the vegetables are slightly softened, 3 to 4 minutes.
Add the wine, olives and their brine, and the potatoes to the pot. Nestle the chicken in the mixture. Bring to a boil, then add 2 cups water and return to a boil. Reduce the heat to medium low, cover and simmer until the chicken is cooked through and the potatoes are tender, about 20 minutes. Season with salt and pepper.
Photograph by Charles Masters
Recipe courtesy of Food Network Magazine