Hydrangea is a tree/shrub rather than a perrenial so no, it cannot be divided.

As Bulbaholic said it's a tree/shrub, best to put it in a bigger pot or even better in the ground, repot Nov to March but March would be best, if in a clay pot I would line it as it would dry out quickly, potted one need lots of water too.

If you want to propagate it hydrangeas often take well from cuttings. I found this video for you: www.youtube.com/watch?v=60M1eSDXdJY

Sorry to disagree with all the others but I have divided an hydrangea that my sister dug up out of her garden for me and the three plants have all grown very well. I have also found that one of my hydrangeas has made roots on some of its stems simply by layering. It's worth a try.

I have managed to split hydrangeas too..but these were in the ground and had spread out over several years. It depends on how big your plant is...If its in a huge pot and its spread over a wide area then get your saw out. but if it's smaller plant it and wit till to see if it spreads.