For the Chicken Broth (adapted and simplified from Tyler Florence)
Place the chicken in a large pot over medium heat with enough water to cover the chicken and allow it to slowly come to a boil.
Add salt, lower the heat to medium-low and gently simmer for 1 to 1½ hours, partially covered, until the chicken is done. As it cooks, skim any impurities that rise to the surface; add a little more water if necessary to keep the chicken covered while simmering.
Carefully remove the chicken to a cutting board. When its cool enough to handle, discard the remaining skin and bones and hand-shred the meat.
Carefully strain the stock to remove any remaining solids.
For the Chicken Noodle Soup
In the same pot where you´ve cooked the broth, add the vegetables and let them simmered in the broth for about 30 minutes.
Add the noodles, salt to taste and let cook until done (normally 7 minutes).