  We report on vibrational ground-state cooling of a single neutral atom
coupled to a high-bandwidth Fabry-P\'erot cavity. The cooling process relies on
degenerate Raman sideband transitions driven by dipole trap beams, which
confine the atoms in three dimensions. We infer a one-dimensional motional
ground state population close to $90~\%$ by means of Raman spectroscopy.
Moreover, lifetime measurements of a cavity-coupled atom exceeding 40 s imply
three-dimensional cooling of the atomic motion, which makes this
resource-efficient technique particularly interesting for cavity experiments
with limited optical access.
