Despite being an important biomedical model species for social behavior, the natural population history of the coppery titi monkey ( Plecturocebus cupreus ) remains largely uncharacterized, in part due to the scarcity of genomic resources available for the species. Apart from the inherent interest in the demographic dynamics of this abundant platyrrhine native to the Amazon forest of Brazil and Peru, this quantification will also serve as a central component of future genotype-to-phenotype studies, given the ability of historical population size change and structure to generate genetic associations. In this study, we deep-sequenced the genomes of six unrelated individuals and inferred a baseline demographic model based on observed levels and patterns of variation in the non-coding regions of the genome. In characterizing these demographic dynamics, we found that estimated population size changes correspond well to previously described speciation times as well as to large-scale climatic changes relating to glaciation patterns.