Loop-erased random walk and its scaling limit, Schramm-Loewner evolution, have found numerous applications in mathematics and physics. We present a 2-dimensional analogue of LERW, the loop erased random surface. We do this by defining a 2-dimensional spanning tree and declaring that LERS should have the same relation to these 2-trees as LERW has to ordinary spanning trees. Furthermore we present numerical evidence that the growth rate for LERS on a $\delta$-fine grid as $\delta \to 0$ is approximately 2.53. This suggests the possibility of a fractal limiting object for LERS analogous to SLE for LERW.