In a large pot add chicken, breast side down, onion, thyme, bay leaf, and garlic. Add enough water to cover; season with salt and pepper. Bring to a boil over high heat; reduce to a simmer, and cook, partially covered, until chicken is cooked through, about 45 minutes. Skim any foam that rises to the top and discard.
Remove chicken from pot, and let stand until cool enough to handle. Skim fat from surface of soup, if desired, and discard. Remove meat from bones; discard skin and bones. Shred meat into bite-size pieces, and return to pot.
Add celery, carrots, potato, egg noodles and parsley. Cook until tender, about 20 minutes. Squeeze fresh limejuice into soup and stir. Can also squeeze into individual bowls before serving.