  We report the first mass and distance measurement of a caustic-crossing
binary system OGLE-2014-BLG-1050L using the space-based microlens parallax
method. \emph{Spitzer} captured the second caustic-crossing of the event, which
occurred $\sim$10 days before that seen from Earth. Due to the coincidence that
the source-lens relative motion was almost parallel to the direction of the
binary-lens axis, the four-fold degeneracy, which was known before only to
occur in single-lens events, persists in this case, leading to either a
lower-mass (0.2 $M_\odot$ and 0.07 $M_\odot$) binary at $\sim$1.1 kpc or a
higher-mass (0.9 $M_\odot$ and 0.35 $M_\odot$) binary at $\sim$3.5 kpc.
However, the latter solution is strongly preferred for reasons including
blending and lensing probability. OGLE-2014-BLG-1050L demonstrates the power of
microlens parallax in probing stellar and substellar binaries.
