Consensus on the evolutionary relationships of humans, chimpanzees, and gorillas has not been reached, despite the existence of a number of DNA sequence data sets relating to the phylogeny, partly because not all gene trees from these data sets agree. However, given the well-known phenomenon of gene tree-species tree mismatch, agreement among gene trees is not expected. A majority of gene trees from available DNA sequence data support one hypothesis, but is this evidence sufficient for statistical confidence in the majority hypothesis? All available DNA sequence data sets showing phylogenetic resolution among the hominoids are grouped according to genetic linkage of their corresponding genes to form independent data sets. Of the 14 independent data sets defined in this way, 11 support a human-chimpanzee clade, 2 support a chimpanzee-gorilla clade, and one supports a human-gorilla clade. The hypothesis of a trichotomous speciation event leading to Homo; Pan, and Gorilla can be firmly rejected on the basis of this data set distribution. The multiple-locus test (Wu 1991), which evaluates hypotheses using gene tree-species tree mismatch probabilities in a likelihood ratio test, favors the phylogeny with a Homo-Pan clade and rejects the other alternatives with a P value of 0.002. When the probabilities are modified to reflect effective population size differences among different types of genetic loci, the observed data set distribution is even more likely under the Homo-Pan clade hypothesis. Maximum-likelihood estimates for the time between successive hominoid divergences are in the range of 300,000-2,800,000 years, based on a reasonable range of estimates for long-term hominoid effective population size and for generation time. The implication of the multiple-locus test is that existing DNA sequence data sets provide overwhelming and sufficient support for a human-chimpanzee clade: no additional DNA data sets need to be generated for the purpose of estimating hominoid phylogeny. Because DNA hybridization evidence (Caccone and Powell 1989) also supports a Homo-Pan clade, the problem of hominoid phylogeny can be confidently considered solved.