The origin of eukaryotes remains unclear1-4. Current data suggest that eukaryotes may have emerged from an archaeal lineage known as `Asgard' archaea5,6. Despite the eukaryote-like genomic features that are found in these archaea, the evolutionary transition from archaea to eukaryotes remains unclear, owing to the lack of cultured representatives and corresponding physiological insights. Here we report the decade-long isolation of an Asgard archaeon related to Lokiarchaeota from deep marine sediment. The archaeon—`Candidatus Prometheoarchaeum syntrophicum' strain MK-D1—is an anaerobic, extremely slow-growing, small coccus (around 550 nm in diameter) that degrades amino acids through syntrophy. Although eukaryote-like intracellular complexes have been proposed for Asgard archaea6, the isolate has no visible organelle-like structure. Instead, Ca. P. syntrophicum is morphologically complex and has unique protrusions that are long and often branching. On the basis of the available data obtained from cultivation and genomics, and reasoned interpretations of the existing literature, we propose a hypothetical model for eukaryogenesis, termed the entangle-engulf-endogenize (also known as E3) model.