We illuminate the nature of the three-dimensional random walks of microorganisms composed of individual organisms adhered together. Such \(aggregate~random~walkers\) are typified by choanoflagellates, eukaryotes that are the closest living relatives of animals. In the colony-forming species \(Salpingoeca~rosetta\) we show that the beating of each flagellum is stochastic and uncorrelated with others, and the vectorial sum of the flagellar propulsion manifests as stochastic helical swimming. A quantitative theory for these results is presented and species variability discussed.