They do exist! Or, at least, they did a few million years ago — and they didn’t look like this (courtesy of a frame grab from The Princess Bride):
They looked more like this:
But they were still big fellas — three meters long, weighing nearly a ton, with a skull half a meter in length. This is about 10 times the size of the largest living rodent (the capybara), and basically comparable in size to a steer or buffalo.
But of course, he ran with large company. About the time that the dinosaurs died out, some 65 million years ago, South America was an island. As a result, animals there could grow to now-amazing sizes — lacking competition or predation from a different stock of animals that were evolving on their own in North America. So South America was, for a time, the home to all sorts of huge animals. It hosted carnivorous birds 3 meters tall, huge crocodiles, and armadillos the size of cars. But then the land-bridge to North America reformed, South American fauna again faced competition and predation from their neighbors to the north, and giant mammals just didn’t have a place any more — as far as evolution was concerned, the party was over. This newly discovered rodent was probably among the last of the South American megafauna.
The latest find (namely, the rodent’s skull) was made in a boulder on the coast of Uruguay, so it’s likely that little more of this particular individual will be found. But other, somewhat smaller rodent fossils have been found in the past decade, so we’ll just have to wait and see how many more critters like him are eventually found elsewhere in South America.
The Royal Society has also made the paper describing the find freely available in PDF — it’s very readable, so check it out.