In a 5- to 6 quart pan, combine the chestnuts, 1 cup grapes, and 2 cups chicken broth. Remove sausage from casing and crumble into pan.
Bring to a boil over high heat, cover, and simmer over medium heat until chestnuts are very soft and mash easily, about 30 minutes. Drain broth into a glass measure and add enough more broth to make 2 cups.
Whirl chestnut mixture in a food processor until smoothly puréed, then whirl in enough broth to give mixture the consistency of softly mashed potatoes. Or whirl mixture, a portion at a time, in a blender, adding enough broth to facilitate puréeing, then more for the desired consistency. Chestnuts continue to thicken as they stand.
Return purée to pan and stir over medium heat until steaming, 2 to 3 minutes; keep warm.
In 10- to 12-inch frying pan over high heat, melt butter and add remaining grapes. Swirl just until fruit is warm and brighter green, about 1 1/2 minutes.
Scrape chestnut purée into a deep bowl and pour grapes on top.