How can I chop onions without crying?
Can't comment directly due to rep limit, but I'm not sure Ryan Elkins above is correct. I'm fairly certain both allinase and LFS are found throughout the layers, though the "core" might contain a higher concentration. Certainly there's no gas contained in the central bulb.

There's a couple of basic strategies for avoiding eye irritation:

Avoid breaking cell walls: use a sharp knife

The enzymes and amino acids involved in producing the Onion Lachrymatory Factor (seriously!) are normally contained in the cells, and only become a problem when released in volume. Using a sharper knife will avoid mangling cell walls, creating more clean separations between layers, and reducing the amount of enzymes released.

Slow down the reaction: refrigerate/freeze the onion

I would guess the activity of both enzymes involved here peaks somewhere around room temperature, or maybe a little higher. You want to get out of this optimum range: either freeze the onion, or heat it beyond denaturation. The former is probably way more practical, since heating to denaturation will leave a soggy mess instead of an onion. You may also be able to deactivate the allinase by substantially altering the pH, for example by coating your knife in lye (not recommended) or lemon juice.

Avoid the reaction products: cut underwater or ventilate

The OLF and the reaction intermediaries look to be fairly water soluble, so cutting under running water should take care of them with sufficient flow rate. 

I'm not sure what the mechanism behind the common candle suggestion is, OLF is a thial oxide and not very flammable. My best guess is that the rising air draws some of the irritant up and away from the area, but in that case a fan should work much better.