The way I fixed the problem was to reduce the swappiness configurable in Ubuntu but, as I was analyzing that, I discovered that both Xorg and Chrome were eating a great deal of memory. As far as I can tell, Xorg bloats due to applications not releasing display memory properly. I figure there's not much I can do about that.
Chrome, however, was another matter. I found a Chrome plugin called OneTab. This product claims to reduce Chrome memory usage by 95%. It accomplishes this by collapsing all the open browser tabs down to one filled with links which, when clicked, restore the tab with no data loss.
It actually seems to work. The only problem is that restored windows don't retain their browser history so you can't use the back button to return to a previous screen after restoring a window. Still, when Chrome has your system crawling, OneTab is a good alternative.