Heat oven to 400°F. Pat the chicken dry inside and out with paper towels. Remove giblet package, if present. Using a paring knife, make a few small cuts in the thickest part of the chicken legs and insert a garlic sliver into each. Being careful not to tear it, use your fingers to gently separate the skin from the breast meat; slide a few slivers of garlic under the skin. Place the remaining garlic and the rosemary sprigs in the chicken cavity. Rub olive oil all over the chicken and sprinkle with kosher salt and pepper. Place chicken in a roasting pan or heatproof baking dish.
Roast, uncovered, for 15 minutes. Add the potatoes to the pan or dish; sprinkle lightly with salt and toss to coat. Continue roasting for 15 minutes more. Stir potatoes. If chicken is browning to fast, cover loosely with foil. Roast another 30 to 40 minutes or until an instant-read thermometer registers 170°F. in the breast or 180°F. in the thigh and potatoes are tender, stirring potatoes once more during cooking.
Remove pan or dish from oven and let stand 10 minutes.