  Mass measurements of gravitational microlenses require one to determine the
microlens parallax $\pie$, but precise $\pie$ measurement, in many cases, is
hampered due to the subtlety of the microlens-parallax signal combined with the
difficulty of distinguishing the signal from those induced by other
higher-order effects. In this work, we present the analysis of the binary-lens
event OGLE-2017-BLG-0329, for which $\pie$ is measured with a dramatically
improved precision using additional data from space-based $Spitzer$
observations. We find that while the parallax model based on the ground-based
data cannot be distinguished from a zero-$\pie$ model at 2$\sigma$ level, the
addition of the $Spitzer$ data enables us to identify 2 classes of solutions,
each composed of a pair of solutions according to the well-known ecliptic
degeneracy. It is found that the space-based data reduce the measurement
uncertainties of the north and east components of the microlens-parallax vector
$\pivec_{\rm E}$ by factors $\sim 18$ and $\sim 4$, respectively. With the
measured microlens parallax combined with the angular Einstein radius measured
from the resolved caustic crossings, we find that the lens is composed of a
binary with components masses of either $(M_1,M_2)\sim (1.1,0.8)\ M_\odot$ or
$\sim (0.4,0.3)\ M_\odot$ according to the two solution classes. The first
solution is significantly favored but the second cannot be securely ruled out
based on the microlensing data alone. However, the degeneracy can be resolved
from adaptive optics observations taken $\sim 10$ years after the event.
