  Consider an instance $h$ of the Gaussian free field on a simply connected
planar domain with boundary conditions $-\lambda$ on one boundary arc and
$\lambda$ on the complementary arc, where $\lambda$ is the special constant
$\sqrt{\pi/8}$. We argue that even though $h$ is defined only as a random
distribution, and not as a function, it has a well-defined zero contour line
connecting the endpoints of these arcs, whose law is SLE(4). We construct this
contour line in two ways: as the limit of the chordal zero contour lines of the
projections of $h$ onto certain spaces of piecewise linear functions, and as
the only path-valued function on the space of distributions with a natural
Markov property.
