The first of two methods I'll describe is shown above. It goes by many different names including an Electrician's Braid and a Doubled Monkey Chain. Parachutists use such a method to keep their chute cords from tangling.
Double up the rope by grasping the two ends together and make a slip noose as shown in step "A". Then, reach through the loop just made and pull a bight of doubled-up rope through it to make a new loop. Continue reaching and pulling loops until you get to step "C".
If you reverse the last move correctly, the whole thing should cleanly unzip with a single tug. This can be tricky sometimes.
Most find it easier to finish the chain by almost pulling the last double loop all the way through, but then taking single bight leftover (the middle of the rope), and and throwing this single bight over the final double bight, as shown in the "Improved Method..." diagram. So when you want to undo it, you just pull on the only single bight available.
This method is especially effective in keeping your rope tangle-free when you need to wash a filthy rope in the washing machine (air-dry only to prevent heat damage). Switching hands halfway through the braid helps reduce kinking at the end.
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