Remove any giblets, rinse the chicken with cold water, and place it into a large saucepan of water. Add 1 teaspoon salt, and bring to a boil over high heat. Reduce heat to a medium low, and simmer about 1 hour, skimming foam from the broth, until the chicken meat is tender.

Mix the flour with a dash of salt in a bowl. With your fingers, make a depression in the top of the flour and drop in the eggs. Add the oil, and stir the eggs into the flour to make a stiff dough. Knead the dough for about 10 minutes, until smooth and elastic, and let it rest, covered, for about 10 minutes.

Cut the dough in half, and roll each piece out, on a well-floured surface, into a rectangle shape until it's about 1/8 of an inch thick. Sprinkle the dough sheet with flour, and roll it up into a loose cylinder. With a sharp knife, cut 1/2 inch wide noodles from the roll. Unroll the noodles, and sprinkle with flour to prevent them from sticking together.

Remove the chicken from the broth and let cool about 10 to 15 minutes, until it's cool enough to handle. Remove the skin and strip all of the meat from the bones, and return the chicken meat to the broth. Bring the broth back to a boil, drop in the fresh noodles, and let simmer over medium-low heat for about 10 minutes, until the noodles are tender, slightly puffed and lighter in color.