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