Any one try vinegar to kill the grass under the fence? I have heard this is effective, but of course have not tried it yet.
We tried white vinegar on weeds several years ago. It worked where the sun was right on the weeds when they were sprayed with the vinegar, and it took a fair amount to do it. That means you really can't use it as selectively as you might want to. For the purpose of clearing a fence line it might be perfect. Boiling water, especially salted, will also work. Nothing will work as fast as chemicals, but the more natural alternatives also won't cause long term damage to the environment.