In Chrome, at the bottom right-hand corner of the window, a little meter appears that shows the percentage of upload. It is just text, not a progress bar.
From my end of things, the problem is solved. It turns out that, since this is a new WordPress install that I was working with, I hadn't yet made the uploads folder writable. Try checking your permissions to see if you are having trouble for the same reason.
The only problem that I am still having is that I am getting a broken image link for the thumbnail in the backend.