Boil clams in clam liquid 5 minutes. Place in container of an electric blender; process until finely chopped.
Combine chopped clams, chicken broth, rice, parsley, and bay leaf in a large Dutch oven; bring to a boil. Reduce heat; cover and cook 25 minutes or until rice is tender. Strain mixture through a sieve into a large bowl; set broth aside.
Remove and discard parsley and bay leaf. Process mixture through a food mill; stir into reserved broth. Strain broth mixture a second time; discard any remaining clam and rice particles in sieve.
Combine strained broth mixture, whipping cream, salt, and pepper in a large Dutch oven; cook over low heat, stirring frequently, until thoroughly heated. (Do not boil.) Ladle into individual soup bowls; serve immediately.