In a large saucepan, cover the wild rice with 2 inches of water and bring to a boil. Boil for 5 minutes, then remove from the heat and let stand for 1 hour. Drain and rinse well.
In a large saucepan of boiling salted water, cook the rice until tender and many of the grains have split, about 30 minutes. Drain well. Wipe out the saucepan.
Melt the butter in the saucepan. Add the wild rice, chestnuts and all but 2 tablespoons of the scallions and cook over moderate heat for 2 minutes. Add the broth and cranberries and cook, stirring occasionally, until the liquid is absorbed, about 15 minutes. Stir in the parsley and reserved scallions and season with salt and pepper. Transfer to a bowl and serve.
The wild rice can be refrigerated overnight and reheated.