  A leading contender for the pairing symmetry in the Fe-pnictide high
temperature superconductors is extended s-wave $s_\pm$, a nodeless state in
which the pairing changes sign between Fermi surfaces. Verifying such a pairing
symmetry requires a special phase sensitive probe that is also momentum
selective. We show that the sign structure of $s_\pm$ pairing leads to surface
Andreev bound states at the sample edge. In the clean limit they only occur
when the edge is along the nearest neighbor Fe-Fe bond, but not for a diagonal
edge or a surface orthogonal to the c-axis. In contrast to d-wave Andreev bound
states, they are not at zero energy and, in general, do not produce a zero bias
tunneling peak. Consequences for tunneling measurements are derived, within a
simplified two band model and also for a more realistic five band model.
