Genome sequences of diverse free-living protists are essential for understanding eukaryotic evolution and molecular and cell biology. The free-living amoeboflagellate Naegleria gruberi belongs to a varied and ubiquitous protist clade (Heterolobosea) that diverged from other eukaryotic lineages over a billion years ago. Analysis of the 15,727 protein-coding genes encoded by Naegleria’s 41 Mb nuclear genome indicates a capacity for both aerobic respiration and anaerobic metabolism with concomitant hydrogen production, with fundamental implications for the evolution of organelle metabolism. The Naegleria genome facilitates substantially broader phylogenomic comparisons of free-living eukaryotes than previously possible, allowing us to identify thousands of genes likely present in the pan-eukaryotic ancestor, with 40% likely eukaryotic inventions. Moreover, we construct a comprehensive catalog of amoeboid-motility genes. The Naegleria genome, analyzed in the context of other protists, reveals a remarkably complex ancestral eukaryote with a rich repertoire of cytoskeletal, sexual, signaling, and metabolic modules.