Determining the relationships among the major groups of cellular life is important for understanding the evolution of biological diversity, but is difficult given the enormous time spans involved. In the textbook 'three domains' tree based on informational genes, eukaryotes and Archaea share a common ancestor to the exclusion of Bacteria. However, some phylogenetic analyses of the same data have placed eukaryotes within the Archaea, as the nearest relatives of different archaeal lineages. We compared the support for these competing hypotheses using sophisticated phylogenetic methods and an improved sampling of archaeal biodiversity. We also employed both new and existing tests of phylogenetic congruence to explore the level of uncertainty and conflict in the data. Our analyses suggested that much of the observed incongruence is weakly supported or associated with poorly fitting evolutionary models. All of our phylogenetic analyses, whether on small subunit and large subunit ribosomal RNA or concatenated protein-coding genes, recovered a monophyletic group containing eukaryotes and the TACK archaeal superphylum comprising the Thaumarchaeota, Aigarchaeota, Crenarchaeota and Korarchaeota. Hence, while our results provide no support for the iconic three-domain tree of life, they are consistent with an extended eocyte hypothesis whereby vital components of the eukaryotic nuclear lineage originated from within the archaeal radiation.