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., $q=1.5times 10^{-3}$ vs. $q=0.6times 10^{-3}$. 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.
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