Melt the butter in a large saucepan over medium heat. Add the leek and carrot, cover and cook 5 minutes. Uncover and add the white pepper. Cook 5 minutes more or until tender. Stir in wine.
Add celeriac, broth, water, salt, and black pepper; bring to a boil. Cover and cook, 10 minutes or until the celeriac is tender.
Place 1 cup of the soup mixture into a blender. remove the center bieces of the blender lid (to allow steam to escape); secure blender lid on blender. Place a clean towel over the opening in the blender lid to avoid splatters. Blend until smooth. Add the pureed soup mixture back to the saucepan.
Add the cooked wild rice; cook for 15 minutes. Spoon into soup bowls and sprinkle with chives.