Gene duplication is an important source of phenotypic change and adaptive evolution. We leverage a haploid hydatidiform mole to identify highly identical sequences missing from the reference genome, confirming that the cortical development gene Slit-Robo Rho GTPase-activating protein 2 (SRGAP2) duplicated three times exclusively in humans. We show that the promoter and first nine exons of SRGAP2 duplicated from 1q32.1 (SRGAP2A) to 1q21.1 (SRGAP2B) ∼3.4 million years ago (mya). Two larger duplications later copied SRGAP2B to chromosome 1p12 (SRGAP2C) and to proximal 1q21.1 (SRGAP2D) ∼2.4 and ∼1 mya, respectively. Sequence and expression analyses show that SRGAP2C is the most likely duplicate to encode a functional protein and is among the most fixed human-specific duplicate genes. Our data suggest a mechanism where incomplete duplication created a novel gene function - antagonizing parental SRGAP2 function - immediately "at birth" 2-3 mya, which is a time corresponding to the transition from Australopithecus to Homo and the beginning of neocortex expansion.