  We show that Earth mass planets orbiting stars in the Galactic disk and bulge
can be detected by monitoring microlensed stars in the Galactic bulge. The star
and its planet act as a binary lens which generates a lightcurve which can
differ substantially from the lightcurve due only to the star itself. We show
that the planetary signal remains detectable for planetary masses as small as
an Earth mass when realistic source star sizes are included in the lightcurve
calculation. These planets are detectable if they reside in the ``lensing zone"
which is centered between 1 and 4 AU from the lensing star and spans about a
factor of 2 in distance. If we require a minimum deviation of 4\% from the
standard point-lens microlensing lightcurve, then we find that more than 2\% of
all $\mearth$ planets and 10\% of all $10\mearth$ in the lensing zone can be
detected. If a third of all lenses have no planets, a third have $1\mearth$
planets and the remaining third have $10\mearth$ planets then we estimate that
an aggressive ground based microlensing planet search program could find one
earth mass planet and half a dozen $10\mearth$ planets per year.
