  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
($M_1 = 170^{+40}_{-50} M_J$ and $M_2 = 110^{+20}_{-30} M_J$), or well below
($M_1 = 22.5^{+0.7}_{-0.4} M_J$ and $M_2 = 13.3^{+0.4}_{-0.3} M_J$) 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 ten years through infrared adaptive-optics imaging with a 40 m
class telescope.
