  We search for runaway stars in the Large Magellanic Cloud (LMC) by computing
the space velocities of the visually brightest stars in the LMC that are
included in the Gaia TGAS proper motion catalog. We compare with predictions
from stellar dynamical models to obtain (peculiar) velocities relative to their
local stellar environment. Two of the 31 stars have unusually high proper
motions. Of the remaining 29 stars we find that most objects in this sample
have velocities in very good agreement with model predictions of a circularly
rotating disk model. Indeed the excellent fit to the model implies that the
TGAS uncertainty estimates are likely overestimated. The fastest outliers in
this subsample contain the LBV R71 and a few other well known emission line
objects though in no case do we derive velocities consistent with fast (~100
km/s) runaways. Our results imply that R 71 in particular has a moderate
deviation from the local stellar velocity field (40 km/s) lending support to
the proposition that this object cannot have evolved as a normal single star
since it lies too far from massive star forming complexes to have arrived at
its current position during its lifetime. Our findings therefore strengthen the
case for this LBV being the result of binary evolution. Of the two stars with
unusually high proper motions we find that one, the isolated B1.5 Ia+
supergiant Sk-67 2 (HIP 22237), is a candidate hypervelocity star, the TGAS
proper motion implying a very large peculiar transverse velocity (~360 km/s)
directed radially away from the LMC centre. If confirmed, for example by Gaia
Data Release 2, it would imply that this massive supergiant, on the periphery
of the LMC, is leaving the galaxy where it will explode as a supernova.
