Two patterns from large-scale DNA sequence data have been put forward as evidence that speciation between humans and chimpanzees was complex, involving hybridization and strong selection. First, divergence between humans and chimpanzees varies considerably across the autosomes. Second, divergence between humans and chimpanzees (but not gorillas) is markedly lower on the X chromosome. Here, we describe how simple speciation and neutral molecular evolution explain both patterns. In particular, the wide range in autosomal divergence is consistent with stochastic variation in coalescence times in the ancestral population; and the lower human-chimpanzee divergence on the X chromosome is consistent with species differences in the strength of male-biased mutation caused by differences in mating system. We also highlight two further patterns of divergence that are problematic for the complex speciation model. Our conclusions raise doubts about complex speciation between humans and chimpanzees.