Remove the chicken from the stock. Strain the stock then return it with the chicken to a clean pot, retaining enough of the broth for another pot for your leeks. Bring the stock up to a gentle simmer. Allow the immersed chicken to heat through thoroughly for 30 minutes; you will now have a moist bird that is not falling apart or toughened from hard boiling. Bring the stock for the leeks to the boil, drop them in, and cook them for about 8–10 minutes, depending on their size.