  Accretion at super-Eddington rates is expected to be accompanied by strong
outflows. Such outflows are observed in Galactic X-ray binaries and
extragalactic Ultra-luminous X-ray sources (ULXs). However, due to their large
source distances, ULX outflows are challenging to detect and study in detail.
Galactic neutron stars accreting from a Be-star companion at super-Eddington
rates show many similarities to ULX pulsars, and therefore offer an alternative
approach to study outflows in this accretion regime. Here, we present Chandra
high-resolution spectroscopy of such a super-Eddington accreting neutron star,
Swift J0243.6+6124, to search for wind outflow signatures during the peak of
its 2017/2018 giant outburst. We detect narrow emission features at rest from
Ne, Mg, S, Si, and Fe. In addition, we detect a collection of absorption
features which can be identified in two ways: either as all Fe transitions at
rest (with a possible contribution from Mg), or a combination of three
blue-shifted Ne and Mg lines at $\sim 0.22c$, while the remaining lines are at
rest. The second scenario would imply an outflow with a velocity similar to
those seen in ULXs, including the ULX pulsar NGC 300 ULX-1. This result would
also imply that Swift J0243.6+6124 launches both a jet, detected in radio and
reported previously, and an ultra-fast wind outflow simultaneously at
super-Eddington accretion rates.
