  We investigate whether the "close/wide" class of degeneracies in
caustic-crossing binary microlensing events can be broken astrometrically.
Dominik showed that these degeneracies are particularly severe because they
arise from a degeneracy in the lens equation itself rather than a mere
"accidental" mimicking of one light curve by another. A massive observing
campaign of five microlensing collaborations was unable to break this
degeneracy photometrically in the case of the binary lensing event MACHO
98-SMC-1. We show that this degeneracy indeed causes the image centroids of the
wide and close solutions to follow an extremely similar pattern of motion
during the time when the source is in or near the caustic. Nevertheless, the
two image centroids are displaced from one another and this displacement is
detectable by observing the event at late times. Photometric degeneracies
therefore can be resolved astrometrically, even for these most severe cases.
