Not the Geneva Convention, but the Geneva Protocol prohibits chemical weapons. It's full name is the Protocol for the Prohibition of the Use in War of Asphyxiating, Poisonous or other Gases, and of Bacteriological Methods of Warfare.

Basically, any usage of Chemical or Biological weapons - but technically not nuclear weapons, though I suppose that radiological weapons would be prohibited - is breaking the Protocol.

Tear gas, and other lachrymators are a grey area, but they are not usually treated in the same way that, say, Sarin would.

However, the production of biological, chemical, and radiological weapons is not prevented under the Protocol, which is how Hitler managed to acquire his chemical weapons, including Zyklon B, for his terrible course of genocide.

Production, storage and transfer is regulated by the the 1972 Biological Weapons Convention (BWC) and the 1993 Chemical Weapons Convention (CWC).