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 in 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 .