  We report a statistically significant detection of nongravitational
acceleration on the sub-kilometer near-Earth asteroid (523599) 2003 RM. Due to
its orbit, 2003 RM experiences favorable observing apparitions every 5 years.
Thus, since its discovery, 2003 RM has been extensively tracked with
ground-based optical facilities in 2003, 2008, 2013, and 2018. We find that the
observed plane-of-sky positions cannot be explained with a purely
gravity-driven trajectory. Including a transverse nongravitational acceleration
allows us to match all observational data, but its magnitude is inconsistent
with perturbations typical of asteroids such as the Yarkovsky effect or solar
radiation pressure. After ruling out that the orbital deviations are due to a
close approach or collision with another asteroid, we hypothesize that this
anomalous acceleration is caused by unseen cometary outgassing. A detailed
search for evidence of cometary activity with archival and deep observations
from Pan-STARRS and the VLT does not reveal any detectable dust production.
However, the best-fitting H$_2$O sublimation model allows for brightening due
to activity consistent with the scatter of the data. We estimate the production
rate required for H$_2$O outgassing to power the acceleration, and find that,
assuming a diameter of 300 m, 2003 RM would require Q(H$_2$O)$\sim10^{23}$
molec s$^{-1}$ at perihelion. We investigate the recent dynamical history of
2003 RM and find that the object most likely originated in the mid-to-outer
main belt ($\sim86\%$) as opposed to from the Jupiter-family comet region
($\sim11\%$). Further observations, especially in the infrared, could shed
light on the nature of this anomalous acceleration.
