  We construct superconformal gauged sigma models with extended rigid
supersymmetry in three dimensions. Those with N>4 have necessarily flat
targets, but the models with N \leq 4 admit non-flat targets, which are cones
with appropriate Sasakian base manifolds. Superconformal symmetry also requires
that the three dimensional spacetimes admit conformal Killing spinors which we
examine in detail. We present explicit results for the gauged superconformal
theories for N=1,2. In particular, we gauge a suitable subgroup of the isometry
group of the cone in a superconformal way. We finally show how these sigma
models can be obtained from Poincare supergravity. This connection is shown to
necessarily involve a subset of the auxiliary fields of supergravity for N \geq
2.
