Rub off as much of the pistachio skins as possible, set nuts aside. In a 4- to 5-quart pan over medium heat, cook the onion, celery, and garlic in the butter until onion is very limp but not brown, about 10 minutes, stir often.
Add sherry, 3/4 cup of the pistachios, broth, rice, parsley, and bay leaf. Bring to a boil, then reduce heat, cover, and simmer until rice is tender to bite, about 25 minutes. Discard bay leaf. In a blender or food processor, whirl soup, a portion at a time, until very smooth, pour through a wire strainer and discard residue. Return soup to pan.
Add cream to soup and stir over medium-low heat until hot, 5 to 7 minutes. Garnish servings with whole chives and sprinkle with the remaining pistachios.