Old fashioned chicken noodle soup

This is a recipe my mom had from somewhere and put in the recipe box she gave me when I left home.

1-3 lb stewing chicken, cut up
2 1/2 tsp salt
1/4 tsp pepper
1/4 tsp dried basil leaves
1 bay leaf
4 sliced carrots - cut into 1" slices
celery to equal amount of carrots - cut into 1" slices
1/2 lb small white onions - washed and peeled (or regular white onion diced large to equal amount of carrots)
1 C fine noodles, uncooked (I use wide egg noodles)

Wash chicken, place in large pot and cover with water. Add seasonings, simmer covered for 1 1/2 hours or until chicken is tender. remove chicken from pot. Prepare vegetables, bring stock to a boil and add vegetables. Simmer for 45 minutes. Remove skin and chicken from bones 10 minutes before the vegetables are done. Add noodles and chicken pieces. Cook minutes longer.