Onions contain sulfur compounds that are released as soon as the knife cuts into the vegetable. The substance that causes the greatest trouble is a compound known as prophetical S-oxide, which rises into the air and combines with water in out tear ducts to form stinging sulfuric acid, which is what makes us cry.
This is why the only way to stop chopping onions being such a tearful business is to prevent all, or at least some, of the oxide from getting into the eyes. This could be done by cutting the onions under water, turning your face away or wearing protective goggles-even wearing contact lenses can help. Also, the more coarsely you chop the onion and the sharper the knife the less oxide is released. It is not clear whether it is also helpful to chill the onion prior to chopping it.