  High-precision astrometry throughout the Local Group is a unique capability
of the Hubble Space Telescope (HST), with potential for transformative science,
including constraining the nature of dark matter, probing the epoch of
reionization, and understanding key physics of galaxy evolution. While Gaia
will provide unparalleled astrometric precision for bright stars in the inner
halo of the Milky Way, HST is the only current mission capable of measuring
accurate proper motions for systems at greater distances (> 80 kpc), which
represents the vast majority of galaxies in the Local Group. The next
generation of proper-motion measurements will require long time baselines,
spanning many years to decades and possibly multiple telescopes, combining HST
with the James Webb Space Telescope (JWST) or the Wide-Field Infrared Survey
Telescope (WFIRST). However, the current HST allocation process is not
conducive to such multi-cycle/multi-mission science, which will bear fruit
primarily over many years. We propose an HST astrometry initiative to enable
long-time-baseline, multi-mission science, which we suggest could be used to
provide comprehensive kinematic measurements of all dwarf galaxies and high
surface-density stellar streams in the Local Group with HST's Advanced Camera
for Surveys (ACS) or Wide Field Camera 3 (WFC3). Such an initiative not only
would produce forefront scientific results within the next 5 years of HST's
life, but also would serve as a critical anchor point for future missions to
obtain unprecedented astrometric accuracy, ensuring that HST leaves a unique
and lasting legacy for decades to come.
