  We report the detection of large-amplitude, rapid radial velocity (RV)
variations and line-splitting in high-resolution Keck/NIRSPEC spectra of the M9
dwarf LP 413-53. We attribute these features to binary motion. Analyzing data
spanning 15 years, we infer a preliminary orbital period of
0.7106156$\pm$0.0000002 day, an eccentricity of 0.0088$\pm$0.0017, a primary RV
semi-amplitude of 23.70$\pm$0.05 km s$^{-1}$, and a secondary RV semi-amplitude
of 28.41$\pm$0.06 km s$^{-1}$, implying a system mass ratio
$M_\mathrm{secondary}$/$M_\mathrm{primary}$ = 0.8340$\pm$0.0017. These
measurements identify LP 413-53 as the shortest-period ultracool binary
discovered to date, and one of the smallest separation main sequence binaries
known. The position and velocity of the system rule out previously reported
membership in the Hyades Moving Group, and indicate that this is likely a pair
of evolved (age $\gtrsim$ 1 Gyr), very-low-mass stars. Assuming masses
consistent with evolved late-M and L dwarfs, we estimate an orbital separation
of 0.0081$-$0.0084 au or 17$-$19 stellar radii, and an orbital inclination
angle of 24$^{\circ}$, making it unlikely that this system exhibits eclipse
events. The larger radii of these stars at young ages would have put them near
contact at the system's current separation, and we speculate that this system
has undergone dynamical evolution, either through orbital angular momentum loss
or ejection of a third component followed by tidal circularization. While
further observations are needed to fully constrain the orbital and physical
parameters of LP 413-53, this ultra-short-period UCD binary system serves as a
new testbed for formation and dynamical evolution models of very-low-mass
multiples.
