In a large pot, combine chicken, carrots, parsnips, and onions. Add water to just cover. Stir in salt. Bring to a boil; reduce to a simmer, and cook, partially covered, until chicken is cooked through, about 35 minutes (skim off foam). Transfer chicken to a plate to cool; refrigerate (see note, below). To serve soup, add noodles to broth, and season with salt, if desired.
To store, pull meat from bones, keeping chicken breasts whole and tearing dark meat into bite-size pieces (discard skin and bones). Refrigerate in separate airtight containers for up to 2 days.