  We validate the planetary nature of an ultra-short period planet orbiting the
M dwarf KOI-4777. We use a combination of space-based photometry from Kepler,
high-precision, near-infrared Doppler spectroscopy from the Habitable-zone
Planet Finder, and adaptive optics imaging to characterize this system.
KOI-4777.01 is a Mars-sized exoplanet ($\mathrm{R}_{p}=0.51 \pm
0.03R_{\oplus}$) orbiting the host star every 0.412-days ($\sim9.9$-hours).
This is the smallest validated ultra-short period planet known and we see no
evidence for additional massive companions using our HPF RVs. We constrain the
upper $3\sigma$ mass to $M_{p}<0.34~\mathrm{M_\oplus}$ by assuming the planet
is less dense than iron. Obtaining a mass measurement for KOI-4777.01 is beyond
current instrumental capabilities.
