KOI-4777 is a cool M-dwarf (about 0.41 solar masses, 3,515 K, 0.40 solar radii), 172 light-years from Earth. KOI-4777.01 is a 0.31-Jupiter-mass companion, with an orbital period of 9.9 hours, at 0.008 AU from its star, and an equilibrium temperature near 1,180 K, discovered in 2022 via transit. The inner world is a hot Jupiter — a gas giant hugging its star at a fraction of Mercury's distance — a class that forced astronomers to rethink how giant planets form and migrate inward. KOI-4777.01 skims its star closer than Mercury orbits the Sun.