Bring all ingredients to a boil in an 8- to 10-quart heavy pot. Skim froth. Reduce heat and gently simmer, uncovered for 3 hours.
Pour stock through a fine-mesh sieve into a large bowl and discard solids. If using stock right away, skim off and discard any fat. If not, cool stock completely, uncovered, before skimming fat, then chill, covered. Reserve a few tablespoons of the skimmed fat (schmaltz) if you wish to use them in matzo balls (below).
Stock can be chilled 3 days in the refrigerator or frozen 1 month.