Image via WikipediaBefore peeling your onion, take off the outer skin like you normally would do. Slice your onion in half and rinse the cut side under cold water for a second or two. Now you can chop your onions tear free!
Another way to keep from crying if you don't have water near by is to place onion halves cut side down on a wooden cutting board. The wood absorbs the juices that would have become air born before they make it to your eyes!