Here we present the hypothesis that increasing copy number (dosage) of sequences encoding DUF1220 protein domains is a major contributor to the evolutionary increase in brain size, neuron number, and cognitive capacity that is associated with the primate order. We further propose that this relationship is restricted to the anthropoid sub-order of primates, with DUF1220 copy number markedly increasing in monkeys, further in apes, and most extremely in humans where the greatest number of copies (~272 haploid copies) is found. We show that this increase closely parallels the increase in brain size and neuron number that has occurred among anthropoid primate species. We also provide evidence linking DUF1220 copy number to brain size within the human species, both in normal populations and in individuals associated with brain size pathologies (1q21-associated microcephaly and macrocephaly). While we believe these and other findings presented here strongly suggest increase in DUF1220 copy number is a key contributor to anthropoid brain expansion, the data currently available rely largely on correlative measures that, though considerable, do not yet provide direct evidence for a causal connection. Nevertheless, we believe the evidence presented is sufficient to provide the basis for a testable model which proposes that DUF1220 protein domain dosage increase is a main contributor to the increase in brain size and neuron number found among the anthropoid primate species and that is at its most extreme in human.