Great suggestions, eltel and Nan, thank you. I looked up pictures of hoya, peperomia, and Ficus benjamina. Of those three, I'm leaning toward ficus because the plant doesn't look succulent at all, but that's difficult to see in the photo. Its stems are woody at the bottom, green and spindly farther up. I found photos of two Ficus benjamina varieties, "Midnight" and "Indigo", that are pretty close.
Thanks, darius, that's good to hear. Now I can figure out how to satisfy the little critter. I'm embarrassed to admit that I pretty much ignored it (except for watering) for almost a year 'til the gardening bug bit me recently.
The picture shows a full grown tree, but you can see the leaves clearly. What throws me is that the leaves in Essensia's picture look like they might be pennate -- pairs of leaves growing directly opposite each other on a stem.
Essensia, are the leave like that, or is it just the pic?
Paris, the leaves are not directly opposite each other. (I originally posted that they're almost directly opposite each other, but I checked, and they're not. Hence the edit to this post.) The tree in your hyperlink looks like a very close match! One weird thing: it indicates "full sun" for the tree, but my plant was in an indoor plant basket created by a florist. Maybe that's why it hardly grew at all in the 8 months I had it at the office?