Chicken Stock:
Combine all of the ingredients in a large pot. Cover and bring to a boil over high heat. Reduce to a bare simmer and cook, partially covered, for an additional 2 hours.
Remove the chicken breasts and reserve. Strain the stock and discard the remaining solids. Remove the meat from the chicken breasts, shred, and store in the refrigerator until ready to use.
Matzo Balls:
Whisk together the schmaltz and the eggs. Stir in the seltzer. Add the remaining ingredients and stir until well combined. Cover and chill, at least an hour or overnight.