Motor tics are a cardinal feature of Tourette syndrome and are traditionally associated with an excess of striatal dopamine in the basal ganglia. Recent evidence increasingly supports a more articulated view where cerebellum and cortex, working closely in concert with basal ganglia, are also involved in tic production. Building on such evidence, this article proposes a computational model of the basal ganglia-cerebellar-thalamo-cortical system to study how motor tics are generated in Tourette syndrome. In particular, the model: (i) reproduces the main results of recent experiments about the involvement of the basal ganglia-cerebellar-thalamo-cortical system in tic generation, (ii) suggests an explanation of the system-level mechanisms underlying motor tic production: in this respect, the model predicts that the interplay between dopaminergic signal and cortical activity contributes to triggering the tic event and that the recently discovered basal ganglia-cerebellar anatomical pathway may support the involvement of the cerebellum in tic production, (iii) furnishes predictions on the amount of tics generated when striatal dopamine increases and when the cortex is externally stimulated. These predictions could be important in identifying new brain target areas for future therapies. Finally, the model represents the first computational attempt to study the role of the recently discovered basal ganglia-cerebellar anatomical links. Studying this non-cortex-mediated basal ganglia-cerebellar interaction could radically change our perspective about how these areas interact with each other and with the cortex. Overall, the model also shows the utility of casting Tourette syndrome within a system-level perspective rather than viewing it as related to the dysfunction of a single brain area.