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.