Depending on the presence or absence of sulci and convolutions, the brains of mammals are classified as gyrencephalic or lissencephalic. We analyzed the encephalic anatomy of the hystricomorph rodent <i>Lagostomus maximus</i> in comparison with other evolutionarily related species. The encephalization quotient (EQ), gyrencephaly index (GI), and minimum cortical thickness (MCT) were calculated for the plains vizcacha as well as for other myomorph and hystricomorph rodents. The vizcacha showed a gyrencephalic brain with a sagittal longitudinal fissure that divides both hemispheres, and 3 pairs of sulci with bilateral symmetry; that is, lateral-rostral, intraparietal, and transverse sulci. The EQ had one of the lowest values among Hystricomorpha, while GI was one of the highest. Besides, the MCT was close to the mean value for the suborder. The comparison of EQ, GI, and MCT values between hystricomorph and myomorph species allowed the detection of significant variations. Both EQ and GI showed a significant increase in Hystricomorpha compared to Myomorpha, whereas a Pearson’s analysis between EQ and GI depicted an inverse correlation pattern for Hystricomorpha. Furthermore, the ratio between MCT and GI also showed a negative correlation for Hystricomorpha and Myomorpha. Our phylogenetic analyses showed that Hystricomorpha and Myomorpha do not differ in their allometric patterning between the brain and body mass, GI and brain mass, and MCT and GI. In conclusion, gyrencephalic neuroanatomy in the vizcacha could have developed from the balance between the brain size, the presence of invaginations, and the cortical thickness, which resulted in a mixed encephalization strategy for the species. Gyrencephaly in the vizcacha, as well as in other Hystricomorpha, advocates in favor of the proposal that in the more recently evolved Myomorpha lissencephaly would have arisen from a phenotype reversal process.