  We construct the chiral gravitational waves from the $z=2$
Ho\v{r}ava-Lifshitz gravity with gravitational Chern-Simons term in the de
Sitter and Minkowski backgrounds. These gravitational waves which show a
feature of the Ho\v{r}ava-Lifshitz gravity may be related to the generalized
uncertainty principle. In addition, we find the classical and quantum IR-UV
transition rules in the $z=2$ Ho\v{r}ava-Lifshitz gravity.
