  We propose boundary conditions on a two dimensional 6-vertex model, which is
defined on the lightcone lattice for an open string worldsheet. We show that,
in the continuum limit, the degrees of freedom of this 6-vertex model describe
a target space coordinate compactified on a circle of radius R, which is
related to the vertex weights. This conclusion had already been established for
the case of a 6-vertex model on the worldsheet lattice for the propagator of a
closed string. This exercise illustrates how the Bethe ansatz works in the
presence of boundaries, at least of this particular type.
