We describe time-dependent tunneling of massless particles in 1 + 1 dimensional string field theory. Polchinski's description of the classical solutions in terms of the Fermi sea is used to identify the leading instanton contribution connecting the two half-lines. The field theory Lagrangian is proportional to 1/g2, where g is the string coupling constant, but the S-matrix for tunneling from one half-line to the other behaves as exp (-C/g). We note the constant C involves curious boundary contributions and observe that a prescription connecting the two half-lines unifies treatments of the Fermi level above and below the barrier.