How do I get lightmap shadows working for trees?

Hi all,

Trying out Unity for the first time, I made a simple model, with steps and columns, and put a light in the middle of it. I then was able to use the Lightmap function with Bake Scene to cast shadows from the structure. Looked pretty neat.

Then I added a tree to the scene, using the Tree Creator standard asset. I tried to get this to cast shadows as well. However, it is not working. The tree will not cast shadows, even though I mark it as a Static object.

What's the deal?