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.