Melt butter in a large saucepan over medium heat. Add leek and carrot; cover and cook 5 minutes. Uncover and cook 5 minutes or until tender. Stir in wine, scraping pan to loosen browned bits. Add celeriac, broth, 1 cup water, salt, and pepper; bring to a boil. Cover and cook 10 minutes or until celeriac is tender.
Place 1 cup soup mixture in a blender. Remove center piece of blender lid (to allow steam to escape); secure blender lid on blender. Place a clean towel over opening in blender lid (to avoid splatters). Blend until smooth. Add pureed soup mixture back to saucepan. Add wild rice; cook 15 minutes. Sprinkle with chives.