Biomolecular motors offer self-propelled, directed transport in designed microscale networks and can potentially replace pump-driven nanofluidics. However, in existing systems, transportation is limited to the two-dimensional plane. Here we demonstrate fully one-dimensional (1D) myosin-driven motion of fluorescent probes (actin filaments) through 80 nm wide, Al2O3 hollow nanowires of micrometer length. The motor-driven transport is orders of magnitude faster than would be possible by passive diffusion. The system represents a necessary element for advanced devices based on gliding assays, for example, in lab-on-a-chip systems with channel crossings and in pumpless nanosyringes. It may also serve as a scaffold for bottom-up assembly of muscle proteins into actin ordered contractile units, mimicking the muscle sarcomere.