We find the general classical solution of the Das-Jevicki collective field theory, corresponding to a tachyon background in (1 + 1)-dimensional string theory. The solution has a simple interpretation in the equivalent free Fermi theory, as a state with a dynamical Fermi surface. In terms of the variables corresponding to the upper and lower Fermi momenta, the collective field hamiltonian separates into right- and left-moving pieces. As one application, we discuss the tree-level S-matrix. We also describe briefly a number of interesting particular solutions.