  We consider critical percolation on the triangular lattice in a bounded
simply connected domain with boundary conditions that force an interface
between two prescribed boundary points. We say the interface forms a
"near-loop" when it comes within one lattice spacing of itself. We define a new
curve by erasing these near-loops as we traverse the interface. Our Monte Carlo
simulations of this model lead us to conclude that the scaling limit of this
loop-erased percolation interface is conformally invariant and has fractal
dimension 4/3. However, it is not SLE_8/3. We also consider the process in
which a near-loop is when the explorer comes within two lattice spacings of
itself.
