Use this stock to make our Chicken and Kale Soup with White Beans. We added canned broth to fortify the stock's flavor, but you can replace it with water, if you prefer.
In a large stockpot, combine all ingredients. Cover, and bring to a boil over medium-high heat; reduce heat to a very gentle simmer. Cook, uncovered, 1 hour, checking occasionally to make sure the liquid is barely bubbling, and skim surface with a large metal spoon as needed.
Transfer whole chicken to a cutting board. Let cool slightly, and pull meat from the sides. (Reserve meat for another use; store in refrigerator up to 3 days, covered well with plastic wrap.)
Return chicken bones to pot. Place a smaller pot lid on surface of stock to keep ingredients submerged. Simmer until bones fall apart when poked, 2 1/2 to 4 hours. Skim surface as needed.
Prepare a large ice bath. Strain stock through a fine sieve into a large heat-proof bowl, discarding solids. Set bowl in ice bath, and let stock cool to room temperature, stirring frequently.
Transfer stock to airtight containers. Refrigerate at least 8 hours or overnight. With a large metal spoon, skim off and discard fat layer that has collected on the top. If storing, leave fat layer intact (it helps to seal in flavor).
Refrigerate stock in airtight containers for up to three days or freeze for up to six months.