Heat oven to 350 degrees. Tear bread into rough pieces. Place in the bowl of a food processor; pulse until bread is in coarse crumbs, about 30 seconds. Spread crumbs onto a baking sheet. Bake until crumbs are dry and pale golden, about 12 minutes.
Heat butter in a medium skillet over medium heat. When hot, add onion and celery. Cook, stirring occasionally, until onions are softened, about 3 minutes. Push to one side of pan; add chicken livers. Brown chicken livers on both sides, about 5 minutes. Remove pan from heat.
Chop chicken livers into 1/8- to 1/4-inch pieces. Toss in a large bowl with onion, celery, breadcrumbs, chestnuts, rosemary, salt, pepper to taste, cream, cognac, and watercress.
To peel a fresh chestnut, score the flat side with an "x." Simmer the chestnuts in water, or roast at 350 degrees, until shells begin to curl. Using a paring knife, remove shells and skins while chestnuts are hot.