  In this work, we study the Friedmann-Robertson-Walker cosmology in which a
Chaplygin gas is coupled to a non-linear scalar field in the framework of the
Ho\v{r}ava-Lifshitz theory. In writing the action of the matter part, we use
the Schutz's formalism so that the only degree of freedom of the Chaplygin gas
plays the role of an evolutionary parameter. In a minisuperspace perspective,
we construct the Lagrangian for this model and show that in comparison with the
usual Einstein-Hilbert gravity, there are some correction terms coming from the
Ho\v{r}ava theory. In such a set-up and by using of some approximations the
classical dynamics of the model is investigated and some discussions about
their possible singularities are presented. We then deal with the quantization
of the model in the context of the Wheeler-DeWitt approach of quantum cosmology
to find the cosmological wave function. We use the resulting wave functions to
investigate the possibility of the avoidance of classical singularities due to
quantum effects.
