  The Orion Nebula Cluster (ONC) is the nearest site of ongoing massive star
formation, which allows us to study the kinematics and dynamics of the region
in detail and constrain star formation theories. Using HST ACS/WFPC2/WFC3IR and
Keck II NIRC2 data, we have measured the proper motions of 701 stars within an
$\sim6'\times6'$ field of view around the center of the ONC. We have found more
than 10 escaping star candidates, concentrated predominantly at the core of the
cluster. The proper motions of the bound stars are consistent with a normal
distribution, albeit elongated North-South along the Orion filament, with
proper motion dispersions of $(\sigma_{\mu,\alpha^*}, \sigma_{\mu,\delta}) =
(0.83\pm0.02,\,1.12\pm0.03)$ mas yr$^{-1}$ or intrinsic velocity dispersions of
$(\sigma_{v,\alpha^*}, \sigma_{v,\delta}) = (1.57\pm0.04,\,2.12\pm0.06)$ km
s$^{-1}$ assuming a distance of 400 pc to the ONC. The cluster shows no
evidence for tangential-to-radial anisotropy. Our velocity dispersion profile
agrees with the prediction from the observed stellar + gas density profile from
Da Rio et al. (2014), indicating that the ONC is in virial equilibrium. This
finding suggests that the cluster was formed with a low star formation
efficiency per dynamical timescale based on comparisons with current star
formation theories. Our survey also recovered high-velocity IR sources BN, x,
and n in the BN/KL region. The estimated location of the first two sources
$\sim500$ years ago agrees with that of the radio source I, consistent with
their proposed common origin from a multi-stellar disintegration. However,
source n appears to have a small proper motion and is unlikely to have been
involved in the event.
