Antiterrorism Act of 1984 - Amends the Federal criminal code to establish a new Federal offense of terrorism. Defines terrorism as the use of force or violence against a person or property in violation of any criminal law with the intent to intimidate, coerce, or influence a government or person in furtherance of any political or ideological objective.

Makes it a criminal offense to commit, attempt, or threaten to commit an act of terrorism. Increases the penalties for a second or subsequent conviction under this section.

Imposes the death penalty if a death of any person results from the act of terrorism and certain sentencing procedures are met.

Grants the Federal Bureau of Investigation primary authority to investigate violations of this Act. Authorizes Federal, State, and local agencies, including the Army, Navy, and Air Force, to assist in such investigations.