Semiconductor heterostructure nanocrystals, especially with core/shell architectures, are important for numerous applications. Here we show that by decreasing the shell growth rate the morphology of ZnS shells on ZnSe quantum rods can be tuned from flat to islands-like, which decreases the interfacial strain energy. Further reduced growth speed, approaching the thermodynamic limit, leads to coherent shell growth forming unique helical-shell morphology. This reveals a template-free mechanism for induced chirality at the nanoscale. The helical morphology minimizes the sum of the strain and surface energy and maintains band gap emission due to its coherent core/shell interface without traps, unlike the other morphologies. Reaching the thermodynamic controlled growth regime for colloidal semiconductor core/shell nanocrystals thus offers morphologies with clear impact on their applicative potential.