Place chestnuts and water to cover in a small Dutch oven; bring to a boil. Cover and cook 20 minutes. Remove from heat; drain and cool.
Remove shells from chestnuts, and peel; coarsely chop chestnuts. Combine chestnuts and chicken broth in a medium saucepan. Place over medium heat, and bring to a boil. Reduce heat; cover and simmer 1 hour or until chestnuts are tender.
Place chestnut mixture in container of an electric blender; process on high speed until smooth.
Melt butter in a large saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add milk; cook over medium heat, stirring constantly, until mixture is bubbly and begins to thicken. Remove from heat.
Add pureed chestnut mixture, salt, and pepper to cream sauce, beating with a wire whisk. Place over low heat; cook, stirring constantly, until thoroughly heated.
Ladle soup into individual serving bowls; garnish with chopped parsley. Serve immediately.