Place over medium heat a stock pot with the olive oil and when warm add the leeks and cook for 5 minutes, constantly turning. Add the celery and the carrots. Sweat for 2 more minutes and add the remainder of the ingredients. Add water to cover and cook at medium low, with the lid half covering the pot for 45 minutes. Add water if needed.
When all the vegetables are tender, and the chicken fully cooked, remove from the heat and let cool for 15 minutes. In a food processor place all the vegetables and the chicken, or do it in batches, and puree it all.
Return it to the stock pot and keep warm. If it is too thick, more water can be added.
At this point I like to cook in a separate pan some little star pasta, or shells as I would do any other pasta. When done I drain and place some of the pasta in a soup bowl and add the soup over it. Place a dollop of crème Fraiche in the middle if you wish.