In a large saucepan, heat the oil over medium-high heat. Add the chicken, stir to coat and cook until brown on all sides, about 5 minutes. Add the carrots, celery, onions, garlic and leek and continue cooking until the vegetables are a light brown. Add enough water to cover the chicken, and then add the peppercorns, parsley and thyme. Stir to mix and bring to a simmer. Reduce the heat to low and let simmer until the meat falls off the bone, about 2 hours.
Keep the chicken aside and let cool. Keep the stock. Debone and cut the meat in chunks. Strain and skim the fat from the stock. Adjust the seasoning with salt and pepper. (This step can be done the day before.)
Add the potatoes to the stock and cook for 20 minutes. Skim the surface if necessary. Add the pasta and continue cooking until the pasta is al dente, 8 to 10 minutes. Add the chicken chunks. Adjust the seasoning and serve.