  We analyze the limitations imposed by photon counting statistics on
extracting useful information about MACHOs from Earth-based parallax
observations of microlensing events. We find that if one or more large (say
$2.5\,\rm m$) telescopes are dedicated to observing a MACHO event for several
nights near maximum amplification, then it is possible, in principle, to
measure the velocity of the MACHO well enough to distinguish between disk and
halo populations for events with $\omega {A_m}\!^2 \gta 1\,\rm day^{-1}$, where
$\omega^{-1}$ denotes the timescale of the event and $A_m$ denotes its maximum
amplification. Thus, if it turns out to be possible to reduce all other sources
of error to below that of photon statistics, it may be feasible to do useful
Earth-based parallax observations for high amplification events.
