Well, not exactly. But have you seen this Seattle Times article, "It's Not Idaho, but You Can Still Grow Potatoes."
Apparently, with a couple of pieces of lumber, some seed potatoes and a careful eye for watering, you can grow 100 pounds of potatoes in a 4 square foot box. Obviously, something a little more rot resistant would be a good idea if you wanted to do this for years to come. But, I'd say if you were trying this for the first time, why not use wood from pallets. Free and abundant on Craigslist.
Anyway, the end of the article mentions using a container or stacks of tires, but it won't be as easy to harvest potatoes from the bottom. Plus...my yard is still looking a little crazy since all the renovation last year. I don't think a stack of tires is going to help at all aesthetically.