  We report the discovery of microlensing planet OGLE-2017-BLG-0373Lb. We show
that while the planet-host system has an unambiguous microlens topology, there
are two geometries within this topology that fit the data equally well, which
leads to a factor 2.5 difference in planet-host mass ratio, i.e., $q=1.5\times
10^{-3}$ vs. $q=0.6\times 10^{-3}$. We show that this is an "accidental
degeneracy" in the sense that it is due to a gap in the data. We dub it "the
caustic-chirality degeneracy". We trace the mathematical origins of this
degeneracy, which should enable similar degenerate solutions to be easily
located in the future. A Bayesian estimate, based on a Galactic model, yields a
host mass $M=0.25^{+0.30}_{-0.15} M_\odot$ at a distance
$D_L=5.9^{+1.3}_{-1.95}$ kpc. The lens-source relative proper motion is
relatively fast, $\mu=9$ mas/yr, which implies that the host mass and distance
can be determined by high-resolution imaging after about 10 years. The same
observations could in principle resolve the discrete degeneracy in $q$, but
this will be more challenging.
