  We present deep Hubble Space Telescope observations of a new magnetar source,
the soft gamma-repeater SGR 1935+2154, discovered by Swift. We obtained three
epochs of observations: while the source was active in March 2015, during a
quiescent period in August 2015, and during a further active phase in May 2016.
Close to the center of the X-ray error region identified by Chandra we find a
faint (F140W(AB)=25.3) source, which fades by a factor of ~2 over the course of
5 months between the first two epochs of observations, before rebrightening
during the second active period. If this source is indeed the counterpart to
SGR 1935+2154 then it is amongst the faintest yet located for a magnetar. Our
observations are spaced over 1.3 years and enable us to place limits on the
source velocity of $\mu = (60 \pm 40)$ km s$^{-1}$ kpc$^{-1}$; observations on
timescales of a decade can hence probe proper motion limits smaller than the
velocities observed for the majority of pulsars. The comparison of the
optical/IR and X-ray lightcurves of the source suggests that emission in the
two regimes is associated but not directly correlated, offering support for a
magnetospheric versus a fallback disc origin.
