Dice the onion and mince the garlic. Add the onion, garlic, and olive oil to a large pot and sauté over medium heat for about 5 minutes, or until the onions are soft and transparent.
While the onion and garlic are sautéing, wash and slice the carrots and celery. Add them to the pot and continue to sauté for a few minutes more.
Add the chicken breasts to the pot along with the bay leaf, basil, parsley, thyme, some freshly cracked pepper, and eight cups of water. Cover the pot, bring it to a boil over high heat, then reduce the heat to low and simmer for one hour. Make sure the pot continues to simmer for the whole hour. If the heat is turned down too low and it is not bubbling away, the chicken will not shred easily.
After an hour of simmering, remove the chicken from the pot. Using two forks, pull the meat apart, shredding it slightly. Season the broth with salt. Begin with one teaspoon and add more to your liking. The flavor of the broth will really pop once the salt is added.
Add the noodles to the pot, turn the heat up to high, and boil the noodles until tender (about 7 minutes). Return the shredded chicken to the pot. Taste and season again with salt if needed. Serve hot!