The term chiral was introduced by Lord Kelvin over a century ago to describe objects that are distinct from their own mirror image. Chirality is relevant in many scientific areas, but particularly chemistry because different mirror image forms of a molecule famously have different biological properties. Chirality typically arises in molecules due to a rigidly chiral arrangement of covalently bonded atoms. Less generally appreciated is that molecular chirality can arise when molecules are threaded through one another to create a mechanical bond. For example, when two molecular rings with chemically distinct faces are joined like links in a chain the resulting structure is chiral even when the rings themselves are not. We re-examined the symmetry properties of such mechanically axially chiral catenanes and in doing so identified a straightforward route to these molecules from simple building blocks. This also led to the discovery of a previously overlooked mechanical stereogenic unit that can arise when such a ring encircles a dumbbell-shaped axle to generate a rotaxane. These insights allowed us to produce the first highly enantioenriched axially chiral catenane and the same approach gave access to a molecule containing the newly identified noncanonical axially chiral rotaxane motif. With methods to access these structures in hand, the process of exploring their properties and applications can now begin.