  We study graviton non-Gaussianities in the EFT of Inflation. At leading
(second) order in derivatives, the graviton bispectrum is fixed by Einstein
gravity. There are only two contributions at third order. One of them breaks
parity. They come from operators that directly involve the foliation: we then
expect sizable non-Gaussianities in three-point functions involving both
gravitons and scalars. However, we show that at leading order in slow roll the
parity-odd operator does not modify these mixed correlators. We then identify
the operators that can affect the graviton bispectrum at fourth order in
derivatives. There are two operators that preserve parity. We show that one
gives a scalar-tensor-tensor three-point function larger than the one computed
in Maldacena, 2003 if $M^2_{\rm P}A_{\rm s}/\Lambda^2\gg 1$ (where $\Lambda$ is
the scale suppressing this operator and $A_{\rm s}$ the amplitude of the scalar
power spectrum). There are only two parity-odd operators at this order in
derivatives.
