  In three dimensions, the effective action for the gauge field induced by
integrating out a massless Dirac fermion is known to give either a
parity-invariant or a parity-violating result, depending on the regularization
scheme. We construct a lattice formulation of the massless Dirac fermion using
the overlap formalism. We show that the result is parity invariant in contrast
to the formulation using Wilson fermions in the massless limit. This
facilitates a non-perturbative study of three-dimensional massless Dirac
fermions interacting with a gauge field in a parity invariant setting with no
need for fine-tuning.
