The origin of the eukaryotic nucleus is difficult to reconstruct. Eukaryotic organelles (chloroplast, mitochondrion) are eubacterial endosymbionts, but the source of nuclear genes has been obscured by multiple nucleotide substitutions. Using evolutionary parsimony, a newly developed rate-invariant treeing algorithm, the eukaryotic ribosomal rRNA genes are shown to have evolved from the eocytes, a group of extremely thermophilic, sulphur-metabolizing, anucleate cells. The deepest bifurcation yet found separates the reconstructed tree into two taxonomic divisions. These are a proto-eukaryotic group (karyotes) and an essentially bacterial one (parkaryotes). Within the precision of the rooting procedure, the tree is not consistent with either the prokaryotic-eukaryotic or the archaebacterial-eubacterial-eukaryotic groupings. It implies that the last common ancestor of extant life, and the early ancestors of eukaryotes, probably lacked nuclei, metabolized sulphur and lived at near-boiling temperatures.