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Abstract We report the analysis of microlensing event OGLE-2017-BLG-1038, observed by the Optical Gravitational Lensing Experiment, Korean Microlensing Telescope Network, and Spitzer telescopes. The event is caused by a giant source star in the Galactic Bulge passing over a large resonant binary-lens caustic. The availability of space-based data allows the full set of physical parameters to be calculated. However, there exists an eightfold degeneracy in the parallax measurement. The four best solutions correspond to very-low-mass binaries near ( M 1 = 170 − 50 + 40 M J and M 2 = 110 − 30 + 20 M J ), or well below ( M 1 = 22.5 − 0.4 + 0.7 M J and M 2 = 13.3 − 0.3 + 0.4 M J ) the boundary between stars and brown dwarfs. A conventional analysis, with scaled uncertainties for Spitzer data, implies a very-low-mass brown-dwarf binary lens at a distance of 2 kpc. Compensating for systematic Spitzer errors using a Gaussian process model suggests that a higher mass M-dwarf binary at 6 kpc is equally likely. A Bayesian comparison based on a galactic model favors the larger-mass solutions. We demonstrate how this degeneracy can be resolved within the next 10 years through infrared adaptive-optics imaging with a 40 m class telescope.