  A previous spectroscopic study identified the very massive O2 III star VFTS
16 in the Tarantula Nebula as a runaway star based on its peculiar
line-of-sight velocity. We use the Gaia DR2 catalog to measure the relative
proper motion of VFTS 16 and nearby bright stars to test if this star might
have been ejected from the central cluster, R136, via dynamical ejection. We
find that the position angle and magnitude of the relative proper motion (0.338
+/- 0.046 mas/yr, or approximately 80 +\- 11 km/s) of VFTS 16 are consistent
with ejection from R136 approximately 1.5 +/- 0.2 Myr ago, very soon after the
cluster was formed. There is some tension with the presumed age of VFTS 16
that, from published stellar parameters, cannot be greater than 0.9 +0.3/-0.2
Myr. Older ages for this star would appear to be prohibited due to the absence
of He I lines in its optical spectrum, since this sets a firm lower limit on
its effective temperature. The dynamical constraints may imply an unusual
evolutionary history for this object, perhaps indicating it is a merger
product. Gaia DR2 also confirms that another very massive star in the Tarantula
Nebula, VFTS 72 (alias BI253; O2 III-V(n)((f*)), is also a runaway on the basis
of its proper motion as measured by Gaia. While its tangential proper motion
(0.392 +/-0.062 mas/yr or 93 +/-15 km/s) would be consistent with dynamical
ejection from R136 approximately 1 Myr ago, its position angle is discrepant
with this direction at the 2$\sigma$ level. From their Gaia DR2 proper motions
we conclude that the two ~100 solar mass O2 stars, VFTS 16 and VFTS72, are fast
runaway stars, with space velocities of around 100 km/s relative to R136 and
the local massive star population. The dynamics of VFTS16 are consistent with
it having been ejected from R136, and this star therefore sets a robust lower
limit on the age of the central cluster of ~1.3 Myr.
