  The Lorentz reciprocal theorem -- that is used to study various transport
phenomena in hydrodynamics -- is violated in chiral active fluids that feature
odd viscosity with broken time-reversal and parity symmetries. Here we show
that the theorem can be generalized to fluids with odd viscosity by choosing an
auxiliary problem with the opposite sign of the odd viscosity. We demonstrate
the application of the theorem to two categories of microswimmers. Swimmers
with prescribed surface velocity are not affected by odd viscosity, while those
with prescribed active forces are. In particular, a torque-dipole can lead to
directed motion.
