Well, my usual Google searches have proved futile, so... What is this vine? The leaves are 2-3 inches wide and very thick.
Try Peperomia obtusifolia in your next search. Typically, this plant grows with a bit more upright oomph (it isn't a climbing plant at all), so I suspect yours hasn't got much light. Nevertheless, it is a tough plant and yours looks reasonably happy. Check out the following link: http://www.hort.purdue.edu/ext/senior/flowers/Peper72.htm
Thanks! It was actually part of a basket arrangement I rescued, so it will probably do much better now that it's not buried under plants several times its height.
