  We use the "Evolution and Assembly of GaLaxies and their Environments" (
EAGLE ) suite of hydrodynamical cosmological simulations to measure offsets
between the centres of stellar and dark matter components of galaxies. We find
that the vast majority (>95%) of the simulated galaxies display an offset
smaller than the gravitational softening length of the simulations
(Plummer-equivalent $\epsilon = 700$ pc), both for field galaxies and
satellites in clusters and groups. We also find no systematic trailing or
leading of the dark matter along a galaxy's direction of motion. The offsets
are consistent with being randomly drawn from a Maxwellian distribution with
$\sigma \leq 196$ pc. Since astrophysical effects produce no feasible analogues
for the $1.62^{+0.47}_{-0.49}$ kpc offset recently observed in Abell 3827, the
observational result is in tension with the collisionless cold dark matter
model assumed in our simulations.
