Preheat oven to 325 degrees. In a large shallow baking pan toast bread until just dry.
Peel and slice onions. In a large heavy skillet cook onions in butter over moderate heat, stirring occasionally, until golden brown. Rinse canned chestnuts. Chop parsley.
In a large bowl, toss together bread, onions, chestnuts, currants, broth, herbs, and salt and pepper to taste and cool completely.
Stuffing may be made a day ahead and chilled, covered.