  We present a catalog of high-precision proper motions in the Orion Nebula
Cluster (ONC), based on Treasury Program observations with the Hubble Space
Telescope's (HST) ACS/WFC camera. Our catalog contains 2,454 objects in the
magnitude range of $14.2<m_{\rm F775W}<24.7$, thus probing the stellar masses
of the ONC from $\sim$0.4 $M_\odot$ down to $\sim$0.02 $M_\odot$ over an area
of $\sim$550 arcmin$^2$. We provide a number of internal velocity dispersion
estimates for the ONC that indicate a weak dependence on the stellar location
and mass. There is good agreement with the published velocity dispersion
estimates, although nearly all of them (including ours at $\sigma_{v,x}=0.94$
and $\sigma_{v,y}=1.25$ mas yr$^{-1}$) might be biased by the overlapping young
stellar populations of Orion A. We identified 4 new ONC candidate runaways
based on HST and the Gaia DR2 data, all with masses less than $\sim$1
$M_\odot$. The total census of known candidate runaway sources is 10 -- one of
the largest samples ever found in any Milky Way open star cluster.
Surprisingly, none of them has the tangential velocity exceeding 20 km
s$^{-1}$. If most of them indeed originated in the ONC, it may compel
re-examination of dynamical processes in very young star clusters. It appears
that the mass function of the ONC is not significantly affected by the lost
runaways.
