Kingdom: Animalia
Phylum: Chordata
Class: Mammalia
Order: Rodentia
Family: Chinchillidae
Genus: Chinchilla
Species:
* Chinchilla lanigera (Long-tailed Chinchilla)
* Chinchilla brevicaudata (Short-tailed Chinchilla)
So, a chinchilla belongs to the genus Chinchilla and can be either the species Chinchilla lanigera or Chinchilla brevicaudata.