  We show that a parity-breaking uniform (averaged over all directions on the
sky) circular polarization of amplitude $V_{00} \simeq 2.6 \times 10^{-17}\,
\Delta \chi (r/0.06)$ can be induced by chiral gravitational-wave (GW)
background with tensor-to-scalar ratio $r$ and chirality parameter $\Delta\chi$
(which is $\pm1$ for a maximally chiral background). We also show, however,
that a uniform circular polarization can arise from a realization of a
non-chiral GW background that spontaneously breaks parity. The magnitude of
this polarization is drawn from a distribution of root-variance $\sqrt{<
V_{00}^2>} \simeq 1.5\times 10^{-18}\, (r/0.06)^{1/2}$ implying that the
chirality parameter must be $\Delta \chi \gtrsim 0.12 (r/0.06)^{-1/2}$ to
establish that the GW background is chiral. Although these values are too small
to be detected by any experiment in the foreseeable future, the calculation is
a proof of principle that cosmological parity breaking in the form of a chiral
gravitational-wave background can be imprinted in the chirality of the photons
in the cosmic microwave background. It also illustrates how a seemingly
parity-breaking cosmological signal can arise from parity-conserving physics.
