Saute celery, carrot and onions in some vegetable oil in a large stock pot. Add chicken. Cover chicken with water and bring to a boil. Reduce heat and simmer for 1 - 2 hours or until the chicken is falling off the bone.
Remove chicken from stock and let cool. Skim fat. Once chicken has cooled remove from bones and tear or chop into bite size pieces.
Peel potatoes and chop into 1 inch cubes.
To make the noodles mix together flour, salt, pepper and baking soda.
Pour the flour mixture onto your counter. Make a well in the middle and the eggs and butter into the well. Fold the mixture together and add enough warm water until you can make a non-sticky dough ball.
Cut the dough in half and roll it out until it is the size of a cookie sheet. Cut into 1-inch squares with a pizza cutter or knife.
Bring stock back to a boil. Add potatoes. Add dough noodles one at a time by placing them where the bubbles are coming up. Stir in. Cook for 1/2 hour and then add in the chicken and green beans. Simmer for about 10 minutes and serve.