Place meat and liver in a Dutch oven with water to cover; bring to a boil. Cover; reduce heat to low, and simmer 15 minutes. Remove from heat; drain well, reserving broth in a heavy saucepan.
Grind ground chuck and liver with a meat grinder, using the finest blade. Add onion; grind a second time.
Combine meat mixture, flour, salt, and pepper; mix well. Stir in 1/4 cup reserved broth. Bring remaining broth to a boil. Drop mixture by tablespoonfuls into boiling broth, allowing room for expansion. Cover; reduce heat, and simmer 12 minutes. Remove liver nips from broth to a warm serving platter. Repeat procedure with remaining meat mixture.