  We propose a method that can determine the ellipticities of source stars of
microlensing events produced by binary lenses. The method is based on the fact
that the products of the caustic-crossing timescale, $\Delta t$, and the cosine
of the caustic incidence angle of the source trajectory, $\kappa$, of the
individual caustic crossings are different for events involving an elliptical
source, while the products are the same for events associated with a circular
source. The product $\Delta t_\perp =\Delta t \cos\kappa$ corresponds to the
caustic-crossing timescale when the incidence angle of the source trajectory is
$\kappa=0$. For the unique determination of the source ellipticity, resolutions
of at least three caustic crossings are required. Although this requirement is
difficult to achieve under the current observational setup based on
alert/follow-up mode, it will be possible with the advent of future lensing
experiments that will survey wide fields continuously at high cadence. For
typical Galactic bulge events, the difference in $\Delta t_\perp$ between
caustic crossings is of the order of minutes depending on the source
orientations and ellipticities. Considering the monitoring frequency of the
future lensing surveys of $\sim 6$ times/hr and the improved photometry
especially of the proposed space-based survey, we predict that ellipticity
determinations by the proposed method will be possible for a significant
fraction of multiple caustic-crossing binary lens events involving source stars
having non-negligible ellipticities.
