Following previous suggestions of other researchers, this paper discusses t
he prospects for astrometric observation of MACHO gravitational microlensin
g events. We derive the expected astrometric observables for a simple micro
lensing event with either a dark or self-luminous lens and demonstrate that
accurate astrometry can determine the lens mass, distance, and proper moti
on in a very general fashion. In particular, we argue that in limited circu
mstances ground-based, narrow-angle differential astrometric techniques are
sufficient to measure the lens mass directly and other lens properties (di
stance, transverse motion) by applying an independent model for the source
distance and motion. We investigate the sensitivity of differential astrome
try in determining lens parameters by Monte Carlo methods and derive a quas
i-empirical relationship between astrometric accuracy and mass uncertainty.