...it's actually the new Ketchup and Fries plant, AKA TomTato. It is a tomato grafted onto potato rootstock.
Mine is doing quite well. The potato flowers have bloomed. Several of the cherry tomatoes have ripened and been eaten. (Good, too!) This is before any of my other tomatoes have even begun to turn red. Someone suggested maybe the tomato plants are more vigorous precisely because they are grafted onto a strong rootstock. Seems plausible.
I called Territorial Seed to find out if the potato part of the plant needed to have more soil piled on once the potatoes started growing. They said yes, that would work, but it would also work just to let everything keep growing as is. I added some soil, and take it on faith that the potatoes are doing well. (Potato leaves are are mostly on the right hand side of the photo near the base of the plant.)