Holding Countries Accountable for Negligent Chemical and Biological Programs Act This bill authorizes initial, intermediate, and final sanctions against countries that act grossly negligent (i.e., knew or should have known that an act or acts would harm another foreign state) with respect to a chemical or biological weapons program. Before imposing initial sanctions, the President must determine that a country acted with gross negligence. Following such a determination, the President must impose the initial sanctions (e.g., suspending scientific cooperative programs and restricting U.S. government contracting with entities operating in chemical or biological sectors of a sanctioned country). Within 120 days of imposing initial sanctions, the President must determine whether the country has taken adequate steps to redress its sanctionable conduct. If the country has not taken adequate steps, the President must impose intermediate sanctions (e.g., terminating financial assistance and prohibiting arms transactions). Within 210 days of imposing intermediate sanctions, the President must again determine whether the country has taken adequate steps to redress its sanctionable conduct. If the country has not taken adequate steps, the President must impose final sanctions (e.g., prohibiting certain transactions in foreign exchange or transfers of credit or payment). The sanctions may be removed after 12 months if the President certifies a country adequately redressed the sanctionable conduct. The bill also authorizes waivers of the sanctions, subject to certain restrictions. Furthermore, the President must determine and report to Congress about whether China meets the criteria for gross negligence with respect to its chemical or biological weapons program.