The victim, Elle Edwards, was a 26-year-old beautician who was fatally shot but is believed to not have been the intended target of the attack, which also left four men injured.
Chapman denied all charges, including possession of a converted Skorpion submachine gun and handling stolen goods.
Another defendant, Thomas Waring, also pleaded not guilty to two charges related to the case.
Both defendants were remanded into custody until their trial at Liverpool Crown Court, scheduled to begin on June 12.
