  The very small accretion disks in ultra-compact X-ray binaries (UCXBs) are
special laboratories in which to study disk accretion and outflows. We report
on three sets of new (250 ks total) and archival (50 ks) Chandra/HETG
observations of the "dipping" neutron-star X-ray binary 4U 1916$-$053, which
has an orbital period of $P\simeq 50$~minutes. We find that the bulk of the
absorption in all three spectra originates in a disk atmosphere that is
redshifted by $v\simeq 220-290$ $\text{km}$ $\text{s}^{-1}$, corresponding to
the gravitational redshift at radius of $R \sim 1200$ $GM/{c}^{2}$. This shift
is present in the strongest, most highly ionized lines (Si XIV and Fe XXVI),
with a significance of 5$\sigma$. Absorption lines observed during dipping
events (typically associated with the outermost disk) instead display no
velocity shifts and serve as a local standard of rest, suggesting that the
redshift is intrinsic to an inner disk atmosphere and not due to radial motion
in the galaxy or a kick. In two spectra, there is also evidence of a more
strongly redshifted component that would correspond to a disk atmosphere at $R
\sim 70$ $GM/{c}^{2}$; this component is significant at the 3$\sigma$ level.
Finally, in one spectrum, we find evidence of disk wind with a blue shift of $v
= {-1700}^{+1700}_{-1200}$ $\text{km}$ $\text{s}^{-1}$. If real, this wind
would require magnetic driving.
