If you don't have a chain break you can carefully use a grinder and grind down the end of the chain pins where you want to take it apart, then the side will come off. The key word here is "carefully". I've been doing it like this for years.
That is how I got my chain lengthened. I used a 4 1/2" grinder, and I wasn't careful really I just grinded both the ends of the pin off and tore the chain apart. A dremmel would probably work good. Could probably even use a file if not grinder.
Hey make sure that horse shoe thing on the master link is facing the open end the opposit way the chain turns. My chain clip thing flipped out because I had it on backward. Cought on my tire or sprocket cover or something.