  Circular ("V-mode") polarization is expected to be vanishing in the CMB,
since it is not produced in Thomson scattering. However, considering that the
conventional CMB anisotropies are generated via an early universe mechanism
such as inflation or a bouncing scenario, it is possible that circular
polarization could be primordially produced and survive to the surface of last
scattering. We study this in detail, and find a large class of inflationary
models that produce a nearly scale invariant spectrum of scalar V-mode
anisotropies. We study the inflationary production and subsequent evolution via
the Boltzmann hierarchy, and show that V-mode polarization present in the CMB
is suppressed by a factor of at least $10^{10^{20}}$ relative to the primordial
$V$, consistent with expectation of negligible V-mode polarization from
inflation. We consider alternative possibilities for sourcing $V$ primordially,
such as the V-mode polarization induced by circularly polarized primordial
gravitational waves, or producing $V$ after inflation, via new interactions at
recombination.
