I ran HOT water over a peeled onion for several minutes in my sink. Apparently, doing this gently blanches the onion and starts to inactivate the enzyme that makes us tear up. For the first time, I was able to cut an onion with no tears.
I let the hot water run over the onion about 5 minutes. Every now and again, I would feel a tear coming on, so I placed it back under the stream of hot water. This instantly took care of the problem.