We search the complete orangutan genome for regions where humans are more closely related to orangutans than to chimpanzees due to incomplete lineage sorting (ILS) in the ancestor of human and chimpanzees. The search uses our recently developed coalescent hidden Markov model (HMM) framework. We find ILS present in ∼1% of the genome, and that the ancestral species of human and chimpanzees never experienced a severe population bottleneck. The existence of ILS is validated with simulations, site pattern analysis, and analysis of rare genomic events. The existence of ILS allows us to disentangle the time of isolation of humans and orangutans (the speciation time) from the genetic divergence time, and we find speciation to be as recent as 9-13 million years ago (Mya; contingent on the calibration point). The analyses provide further support for a recent speciation of human and chimpanzee at ∼4 Mya and a diverse ancestor of human and chimpanzee with an effective population size of about 50,000 individuals. Posterior decoding infers ILS for each nucleotide in the genome, and we use this to deduce patterns of selection in the ancestral species. We demonstrate the effect of background selection in the common ancestor of humans and chimpanzees. In agreement with predictions from population genetics, ILS was found to be reduced in exons and gene-dense regions when we control for confounding factors such as GC content and recombination rate. Finally, we find the broad-scale recombination rate to be conserved through the complete ape phylogeny.