Preheat the oven to 200°C, fan 180°C, gas 6. Put the potatoes, carrots, garlic, thyme and bay leaf in a roasting tin; drizzle with the oil. Season and toss.
In a bowl, mix together the butter, tarragon, chives and lemon zest; season. Loosen the skin from the breast of the chicken and spread the butter under the skin. Sit the chicken on the veg. Halve the lemon and squeeze the juice into the cavity.
Roast for 20 minutes, then remove from the oven. Add the leeks and pour the wine around the chicken. Reduce the temperature to 180°C, fan 160°C, gas 4 and return the chicken to the oven for 1 hour, or until the juices run clear. Rest for at least 20 minutes, then scatter with the extra tarragon.