Most mobile robots use wheels that perform well on even and structured ground, like in factories and warehouses. However, they face challenges traversing unstructured terrain such as stepped obstacles. This letter presents the design and testing of the PaTS-Wheel: a Passively-Transformable Single-part Wheel that can transform to render hooks when presented with obstacles. The passive rendering of this useful morphological feature is guided purely by the geometry of the obstacle. The energy consumption and vibrational profile of the PaTS-Wheel on flat ground is comparable to a standard wheel of the same size. In addition, our novel wheel design was tested traversing different terrains with stepped obstacles of incremental heights. The PaTS-Wheel achieved 100% success rate at traversing stepped obstacles with heights ≈70% its diameter, higher than the results obtained for an equivalent wheel ( ≈25% its diameter) and an equivalent wheg ( ≈61% its diameter). This achieves the design objectives of combining the energy efficiency and ride smoothness of wheels with the obstacle traversal capabilities of legged robots, all without requiring any sensors, actuators, or controllers.