  Context. Westerlund I is the richest young cluster currently known in our
Galaxy, making it one of the most massive clusters for which we can resolve the
individual stars even in the crowded centre. This makes it an ideal target to
assess whether massive clusters formed currently will remain bound or will
disperse and contribute significantly to the stellar field population. Aims.
Here we report a measurement of the radial velocity dispersion of Westerlund I
to explore whether the cluster is currently in virial equilibrium, if it is in
the process of collapse or if it is expanding and dispersing into the field.
Methods. We obtained MIKE/Magellan high resolution optical spectra of 22 post
main-sequence stars jn Westerlund I for 2 or 3 epochs with a maximum baseline
of about one year. Radial velocities variations between these spectra have been
measured through cross correlation. Results. We calculate the velocity
dispersion from the cross correlation of five yellow hypergiants and one
luminous blue variable, that show little radial velocity variations between
epochs and have many spectral features in common. After taking into account the
effect of small number statistics and undetected binaries, we estimate the
velocity dispersion for the massive stars in Westerlund I to be 2.1 (+3.3,
-2.1) km s-1. For several different assumptions concerning possible mass
segregation and the elongation of the cluster, we find that Westerlund I is
subvirial at the 90% confidence level. Conclusions. We can rule out that the
cluster is significantly supervirial at the 97% confidence level, indicating
that Westerlund I is currently bound. This implies that Westerlund I has
survived past the point where any gas expulsion has taken place and is expected
to survive for billions of years.
