The retrieval of Neanderthal (Homo neanderthalsensis) mitochondrial DNA is thought to be among the most significant ancient DNA contributions to date, allowing conflicting hypotheses on modern human (Homo sapiens) evolution to be tested directly. Recently, however, both the authenticity of the Neanderthal sequences and their phylogenetic position outside contemporary human diversity have been questioned. Using Bayesian inference and the largest dataset to date, we find strong support for a monophyletic Neanderthal clade outside the diversity of contemporary humans, in agreement with the expectations of the Out-of-Africa replacement model of modern human origin. From average pairwise sequence differences, we obtain support for claims that the first published Neanderthal sequence may include errors due to postmortem damage in the template molecules for PCR. In contrast, we find that recent results implying that the Neanderthal sequences are products of PCR artifacts are not well supported, suffering from inadequate experimental design and a presumably high percentage (>68%) of chimeric sequences due to "jumping PCR" events.