HD 106906 is a 15 Myr old short-period (49 days) spectroscopic binary that hosts a wide-separation (737 au) planetary-mass ($sim11,M_{rm Jup}$) common proper motion companion, HD 106906 b. Additionally, a circumbinary debris disk is resolved at optical and near-infrared wavelengths that exhibits a significant asymmetry at wide separations that may be driven by gravitational perturbations from the planet. In this study we present the first detection of orbital motion of HD 106906 b using Hubble Space Telescope images spanning a 14 yr period. We achieve high astrometric precision by cross-registering the locations of background stars with the Gaia astrometric catalog, providing the subpixel location of HD 106906 that is either saturated or obscured by coronagraphic optical elements. We measure a statistically significant $31.8pm7.0$ mas eastward motion of the planet between the two most constraining measurements taken in 2004 and 2017. This motion enables a measurement of the inclination between the orbit of the planet and the inner debris disk of either $36_{-14}^{+27}$ deg or $44_{-14}^{+27}$ deg, depending on the true orientation of the orbit of the planet. There is a strong negative correlation between periastron and mutual inclination; orbits with smaller periastra are more misaligned with the disk plane. With a periastron of $510_{-320}^{+480}$ au, HD 106906 b is likely detached from the planetary region within 100 au radius, showing that a Planet Nine-like architecture can be established very early in the evolution of a planetary system.
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