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. Display omitted ► Missing SRGAP2 human-specific genes sequenced by using haploid hydatidiform mole DNA ► SRGAP2 duplicated three times in the human lineage ∼1.0–3.4 million years ago ► One duplicate is expressed in the brain and is fixed in copy number in all humans ► The incomplete initial duplication likely antagonized the parent gene at birth A series of incomplete duplications of an ancestral neuronal gene that took place only in the human lineage generated truncated genes, likely to encode new functions immediately upon “birth.” The appearance of these human-specific genes coincides with the emergence of an expanded neocortex.