Static Meshes use vertex lighting. It is quite obvious by looking at the lighting on that mesh that there are very few vertices on that side of the mesh. You can see the individual polygons by how they are lit.
You NEED to use more polygons and you NEED to properly distribute/configure them on the model with the lighting in mind. There are tutorials on this I have seen, though I can't remember where, but this is your problem. Also keep in mind that if a vertex is inside the model or other geometry it will not get lit, thus appearing black, so you need to make sure each vertex is 'reachable' by light.