In a medium saucepan, combine chicken, egg whites, carrot, and celery. Stir to combine. Add 2 cups stock; stir to combine. Add remaining 6 cups stock. Place over medium-high heat. Cook, stirring frequently, until mixture comes to a boil and a solid mass has formed on top. There should be liquid and foam bubbling up around the edges. Do not stir once liquid has come to a boil. Reduce to a low simmer, and cook for 45 minutes.
Remove from heat. Ladle only the clear liquid into a damp cheesecloth-lined sieve. Do not press down on solids; just allow the liquid to drip. If any particles remain in broth, strain again in the same manner. The consomme may be chilled until any remaining fat solidifies on the surface. Remove fat, and discard. The consomme will keep refrigerated in an airtight container for 3 days and frozen for up to 3 months.