Autonomous and driven transport in chiral fluids have been shown to exhibit features that cannot be accommodated within the classical formulation of fluid mechanics, due to the role of odd viscosity. We generalize the theory of phoretic active matter to fluid environments with odd viscosity and derive expressions for translational and rotational self-propulsion velocities in the case of a spherical swimmer with arbitrary activity and mobility surface profiles. We discuss specific examples of chemically active colloids with axisymmetric and non-axisymmetric coatings and the resulting interplay between symmetry and chirality. Our results can be applied to study the emergent collective dynamics of phoretic particles in fluid media with broken time-reversal and parity symmetries.