Warm the oil in a deep, lidded pan. Add the chicken pieces skin-side down and lightly seasoned, then cook until the skin is rich, deep gold. Turn them and colour the underside similarly, then remove from the pan and set aside.
Set the oven to 200ºc. Trim the leeks, discarding the roots and very tips of the leaves. Cut into short pieces about the length of a wine cork, then wash thoroughly, removing all grit between the layers.
Pat the leeks dry, then fry them in the chicken pan over a moderate heat for about 5 minutes, covered with a lid, so they soften without browning. Pour in the stock and bring to the boil, stirring as you go, then add the half lemon, and season with salt and pepper. As the stock boils, pour in the pasta and continue boiling for 3 minutes. Return the chicken to the pan, cover again and bake for 35 minutes.
Remove the lid, add the peas, then return to the oven for 5 minutes. Check the seasoning, then add the tarragon and parsley and serve in bowls, with spoons.