  We prove that the chordal contour lines of the discrete Gaussian free field
converge to forms of SLE(4). Specifically, there is a constant lambda > 0 such
that when h is an interpolation of the discrete Gaussian free field on a Jordan
domain -- with boundary values -lambda on one boundary arc and lambda on the
complementary arc -- the zero level line of h joining the endpoints of these
arcs converges to SLE(4) as the domain grows larger. If instead the boundary
values are -a < 0 on the first arc and b > 0 on the complementary arc, then the
convergence is to SLE(4;a/lambda-1,b/lambda-1), a variant of SLE(4).
