Hi, Andy. This is a problem with the lightsource object, not the plane. There is a problem that makes lightsources exceptionally grainy, it doesn't happen with sunlights, though you can't place a sun so close to the camera. I think it needs to be in the extremities of your scene, given that there are no transform controls for it. Dragging the sunlight's transform arrows won't help either.
Enabling ray-traced atmo' and bumping samples up to the heavens(I mean really high, not just the 64-128 samples that you'd normal get away with for grainy scenes, I've still suffered this problem with samples of 256 and higher when using lights) can help this but that will REALLY eat up render time.
I rarely use lightsources for this reason, I just can't justify the render time.
EDIT: Ahh, Mr. Meyer, you beat me to it.