Boil chicken in a large pot for about 20 minutes or until done. Remove chicken and keep the broth in the pot.
Mix flour and 1/2 teaspoon salt in medium bowl. Make a well in cneter of flour mixture. Mix in eggs, 1/4 cup water and the oil thoroughly. (If dough is too dry, min in a few drops water; if dough is too sticky, min in a small amount of flour.)
Gather dough into a ball. Knead on floured surface about 5 minutes or until smooth and elastic.
Divide dough into 4 equal parts. Roll one part at a time into paper-thin rectangle on generously floured surface (keep remaining dough covered). Loosely fold rectangle lengthwise into thirds. Cut crosswise into 1/4-inch strips. Unfold strips and plac ein single layer on towels; let stand at least 30 minutes until dry.
Add 2 cans of chicken broth to large pot of chicken broth already made. Place noodles in boiling broth. Boil uncovered for 3 to 5 minutes or until firm but tender. Begin testing for doneness when pasta rises to surface of water. When done, add 1 can of cream of chicken and shredded cooked chicken. Salt and pepper to taste. Serving suggestion: Place over mashed potatoes and enjoy!