  The formation of the most massive stars in the Universe remains an unsolved
problem. Are they able to form in relative isolation in a manner similar to the
formation of solar-type stars, or do they necessarily require a clustered
environment? In order to shed light on this important question, we study the
origin of two very massive stars (VMS): the O2.5If*/WN6 star RFS7 ($\sim$100
$M_{\odot}$), and the O3.5If* star RFS8 ($\sim$70 $M_{\odot}$), found within
$\approx$ 53 and 58 pc respectively from the Galactic massive young cluster NGC
3603, using Gaia data. RFS7 is found to exhibit motions resembling a runaway
star from NGC 3603. This is now the most massive runaway star candidate known
in the Milky Way. Although RFS8 also appears to move away from the cluster
core, it has proper-motion values that appear inconsistent with being a runaway
from NGC 3603 at the $3\sigma$ level (but with substantial uncertainties due to
distance and age). Furthermore, no evidence for a bow-shock or a cluster was
found surrounding RFS8 from available near-infrared photometry. In summary,
whilst RFS7 is likely a runaway star from NGC 3603, making it the first VMS
runaway in the Milky Way, RFS8 is an extremely young ($\sim$2 Myr) VMS, which
might also be a runaway, but this would need to be established from future
spectroscopic and astrometric observations, as well as precise distances. If
RFS8 were still not meeting the criteria for being a runaway from NGC 3603 from
such future data, this would have important ramifications for current theories
of massive star formation, as well as the way the stellar initial mass function
(IMF) is sampled.
