  In this paper, we study the effects of parity violation on non-gaussianities
of primordial gravitational waves in the framework of Ho\v{r}ava-Lifshitz
theory of gravity, in which high-order spatial derivative operators, including
the ones violating parity, generically appear. By calculating the three point
function, we find that the leading-order contributions to the non-gaussianities
come from the usual second-order derivative terms, which produce the same
bispectrum as that found in general relativity. The contributions from
high-order spatial n-th derivative terms are always suppressed by a factor
$(H/M_*)^{n-2} \; (n \ge 3)$, where $H$ denotes the inflationary energy and
$M_*$ the suppression mass scale of the high-order spatial derivative operators
of the theory. Therefore, the next leading-order contributions come from the
3-dimensional gravitational Chern-Simons term. With some reasonable arguments,
it is shown that this 3-dimensional operator is the only one that violates the
parity and in the meantime has non-vanishing contributions to
non-gaussianities.
