We investigate the electronic structure of twin boundaries in orthorhombically distorted high-T-c, materials using the quasiclassical theory of superconductivity. At low temperatures we find a local instability to a time-reversal symmetry breaking state at the twin boundary. This state yields spontaneous currents along the twin boundary that are microscopically explained by the structure of the quasiparticle bound states. We calculate the local density of states and find a splitting in the zero-bias peak once the spontaneous currents set in. This splitting is measurable by STM techniques and is a unique signature of time-reversal breaking states at a twin boundary.