Organizing inorganic nanocrystals into complex architectures is challenging and typically relies on preexisting templates, such as properly folded DNA or polypeptide chains. We found that under carefully controlled conditions, cubic nanocrystals of magnetite self-assemble into arrays of helical superstructures in a template-free manner with >99% yield. Computer simulations revealed that the formation of helices is determined by the interplay of van der Waals and magnetic dipole-dipole interactions, Zeeman coupling, and entropic forces and can be attributed to spontaneous formation of chiral nanocube clusters. Neighboring helices within their densely packed ensembles tended to adopt the same handedness in order to maximize packing, thus revealing a novel mechanism of symmetry breaking and chirality amplification.