  We consider worldsheet string theory on $Z_N$ orbifolds of $AdS_3$ associated
with conical singularities. If the orbifold action includes a similar twist of
$S^3$, supersymmetry is preserved, and there is a moduli space of vacua arising
from blowup modes of the orbifold singularity. We exhibit the spectrum,
including the properties of twisted sectors and states obtained by fractional
spectral flow. A subalgebra of the spacetime superconformal symmetry remains
intact after the $Z_N$ quotient, and serves as the spacetime symmetry algebra
of the orbifold.
