Rinse the chicken, inside and out, under cold water. Rinse the Smithfield ham under cold water to remove excess salt.

Place the chicken, ham, and pork in a large pot. Add enough water to cover by 1 inch. Bring to a boil over high heat and let boil for 5 minutes. Drain, discarding the liquid. Rinse the chicken, ham, and pork and drain, discarding the liquid.

Return the meats to a clean pot and add the 8 cups water. Bring just to a boil over high heat. Reduce the heat to maintain a gentle simmer. Skim any foam that rises to the surface. Cook covered until the chicken is falling off the bone, about 2 hours.

Strain through a fine-mesh sieve, saving the meat for another use.

Use immediately or let cool, cover, and refrigerate for up to 1 week or freeze for up to 6 months.