  A major problem in the interpretation of microlensing events is that the only
measured quantity, the Einstein time scale t_E, is a degenerate combination of
the three quantities one would like to know, the mass, distance, and speed of
the lens. This degeneracy can be partly broken by measuring either a "parallax"
or a "proper motion" and completely broken by measuring both. Proper motions
can easily be measured for caustic-crossing binary-lens events. Here we examine
the possibility (first discussed by Hardy & Walker) that one could also measure
a parallax for some of these events by comparing the light curves of the
caustic crossing as seen from two observatories on Earth. We derive analytic
expressions for the signal-to-noise ratio of the parallax measurement in terms
of the characteristics of the source and the geometry of the event. For
Galactic halo binary lenses seen toward the LMC, the light curve is delayed
from one continent to another by a seemingly minuscule 15 seconds (compared to
t_E ~ 40 days). However, this is sufficient to cause a difference in
magnification of order 10%. To actually extract complete parallax information
(as opposed to merely detecting the effect) requires observations from three
non-collinear observatories. Parallaxes cannot be measured for binary lenses in
the LMC but they can be measured for Galactic halo binary lenses seen toward
M31. Robust measurements are possible for disk binary lenses seen toward the
Galactic bulge, but are difficult for bulge binary lenses.
