I saw capybara in the swamps in Northern Argentina when I was there. They are huge! Their tracks were the size of my whole hand.
I don't know if they're friendly, or if they can be leash-trained, but if so I would love to have a pet capybara. Just to watch folks wig out. And I bet there aren't any zoning rules against it, just because no one thought of it before.
Now, getting one into the country is a whole 'nother matter.