  We construct, to leading orders in the momentum expansion, an effective
theory of a chiral $p_x + ip_y$ two-dimensional fermionic superfluid at zero
temperature that is consistent with nonrelativistic general coordinate
invariance. This theory naturally incorporates the parity and time reversal
violating effects such as the Hall viscosity and the edge current. The particle
number current and stress tensor are computed and their linear response to
electromagnetic and gravitational sources is calculated. We also consider an
isolated vortex in a chiral superfluid and identify the leading chirality
effect in the density depletion profile.
