  We present a chiral solution of the Ginsparg-Wilson equation. This work is
motivated by our recent proposal for nonperturbatively regulating chiral gauge
theories, where five-dimensional domain wall fermions couple to a
four-dimensional gauge field that is extended into the extra dimension as the
solution to a gradient flow equation. Mirror fermions at the far surface
decouple from the gauge field as if they have form factors that become
infinitely soft as the distance between the two surfaces is increased. In the
limit of an infinite extra dimension we derive an effective four-dimensional
chiral overlap operator which is shown to obey the Ginsparg-Wilson equation,
and which correctly reproduces a number of properties expected of chiral gauge
theories in the continuum.
