  In this work we show that the gravitational Chern-Simons term, aside from
being a key ingredient in inflationary baryogenesis, modifies super-horizon
gravitational waves produced during inflation. We compute the super-Hubble
gravitational power spectrum in the slow-roll approximation and show that its
overall amplitude is modified while its spectral index remains unchanged (at
leading order in the slow-roll parameters). Then, we calculate the correction
to the tensor to scalar ratio, T/S. We find a correction of T/S which is
dependent on $\cal{N}$ (more precisely quadratic in ${\cal N}$), the parameter
characterizing the amplitude of the Chern-Simons terms. In a stringy embedding
of the leptogenesis mechanism, $\cal{N}$ is the ratio between the Planck scale
and the fundamental string scale. Thus, in principle, we provide a direct probe
of leptogenesis due to stringy dynamics in the Cosmic Microwave Background
(CMB). However, we demonstrate that the corresponding correction of T/S is in
fact very small and not observable in the regime where our calculations are
valid. To obtain a sizable effect, we argue that a non-linear calculation is
necessary.
