Joan, With kingianum hybrids, winter is their dormant (and bloom) season. Now isn't the best time to divide them and repot. I do mine in the early spring once temps start to warm up (about when daffodils are in flower). They spent last summer outside - and they loved it!!
I agree with the others that they like to be pot bound, and your plant looks happy the way it is. If that one were mine, I would wait until Spring, then repot (as described by karren) into just a slightly bigger pot. I wouldn't divide it.
If you really have to divide it for some reason, make sure you soak the it for at least 30 minutes to make the roots pliable. It may be difficult to find a natural break in the clump, as the canes can be very crowded together, but if you start pulling apart roughly in the middle, you should find that you can get it to break apart naturally. It may take some time to work your way across the clump like this, but you'll do a lot less damage this way than by chopping it with a knife.
Again, if it were mine, I would just check the middle of the pot for dead roots and broken down medium, removing any that I found. Replace that with fresh medium, slip it into a slightly larger pot and fill in around the edges with more fresh medium new roots can grow into. In my pots for my larger ones, there is about 70% roots, 30% medium.
If you look through this thread,
http://www.orchidboard.com/community...ng-flower.html, I posted some photos of some of my plants. There are a couple of whole plant shots later in the thread too.