Split Mesh

Hello, I have a dynamically created mesh, and I am doing custom LOD'ing. Now to achieve what I want, I have to subdivide the mesh into separate game-objects(chunks), so that I can handle the detail of the chunk individually.

So what I would like to know is, how do I uniformly cut a mesh of one game-object into two separate game objects? The mesh I want to cut in half, is effectively, just a plain face from a cube. So it is just a straight even mesh.

Here's a picture example of what I want to do:

I have this one single mesh, I want to cut it, straight down the center, to create two, separate halves of the original mesh.

Any help is greatly appreciated!