Biological, Chemical, and Radiological Weapons Countermeasures Research Act - Amends the Homeland Security Act of 2002 to add a new title, Title 18: Biological, Chemical, and Radiological Countermeasures Research, which may be cited as the Biological, Chemical, and Radiological Weapons Countermeasures Research Act of 2003.Directs the Secretary of Homeland Security to make available to manufacturers of terror weapons countermeasures, and to publish, a list of materials that may be used as weapons of mass destruction (WMD). Directs the Secretary to revise the list on at least an annual basis. Requires the Secretary to determine countermeasures that diagnose, treat, or prevent infection from biological agents or toxins (countermeasures) for each item on the list.Requires private sector entities that are engaged in certain research to register with the Department of Homeland Security if they wish to benefit from various tax, patent, procurement, liability limitations, and other incentives established under this Act. Classifies such research as: (1) countermeasures; (2) equipment to detect a terrorist attack carried out with a terror weapon (detection equipment); (3) diagnostics to detect, identify, or analyze biological agents or toxins (diagnostics); and (4) research tools used in the laboratory (research tools) that enable the rapid and effective development of countermeasures.Establishes in the Treasury of the United States a "Terror Weapon Countermeasure Purchase Fund (TWCPF)" to purchase, and provide adequate payment for, countermeasures, detection equipment, diagnostics, and research tools.Extends market exclusivity for new drugs that are countermeasures.Authorizes the Director of the National Institutes of Health (NIH) to award partnership challenge grants to promote joint ventures between NIH, its grantees, and for-profit biotechnology, pharmaceutical, and medical device industries for the development of countermeasures and research tools.