Place the potatoes, carrots, garlic cloves, oil and lots of seasoning in a large roasting dish (about 30 x 20cm). Squeeze over all the juice from the lemon halves, then cut them into wedges and add them to the dish. Toss everything together, cover the dish with foil, and roast for about 15 minutes.Remove the foil and add the rosemary sprigs. Season the chicken thighs and add to the roasting dish.
Return to the oven for a further 25-30 minutes until the potatoes are tender, and the chicken is crisp and cooked through.