Heat the butter in a saucepan. Add the leeks and celery and toss together for a few seconds. Add 1/2 cup of the chicken broth. Cover and simmer over low heat for 5 to 10 minutes or until vegetables are tender. Add the remaining broth and rice and bouquet garni. Cover and simmer, over very low heat for 25 minutes or until rice is very tender.
Remove the bouquet garni and puree the soup through a food mill or food processor. Return it to the saucepan, add the lemon juice and season to taste with salt and pepper. If soup is thin, simmer it down until thick enough; if too thick, add some water. Add the chicken and simmer, uncovered, for 5 minutes or until chicken is just cooked through. Adjust the seasoning. Portion out and garnish with parsley.