Heat the oil in a brothpot over medium heat. Add the onions, carrots, and celery and cook, stirring often, until softened, about 10 minutes.
Cut the chicken into 8 pieces. Add the chicken to the pot and pour in the broth. Add enough cold water to cover the ingredients by 2 inches. Bring to a boil over high heat, skimming off the foam that rises to the surface. Add the parsley, thyme, and bay leaf.
Reduce the heat to low. Simmer, uncovered, until the chicken is very tender, about 2 hours.
Remove the chicken from the pot and set aside until cool enough to handle. Remove and discard the parsley and thyme sprigs and bay leaf. Let stand 5 minutes and degrease the soup.
Discard the chicken skin and bones and cut the meat into bite-size pieces. Add the noodles and cook until done, about 10 minutes. Stir the meat back into the soup and season to taste with salt and pepper. Serve hot.