Fascinating phenomena can occur as charge and/or energy carriers are confined in one dimension^1,2,3,4. One such example is the divergent thermal conductivity (κ) of one-dimensional lattices, even in the presence of anharmonic interatomic interactions—a direct consequence of the Fermi–Pasta–Ulam–Tsingou paradox proposed in 1955⁵. This length dependence of κ, also known as superdiffusive phonon transport, presents a classical anomaly of continued interest^6,7,8,9. So far the concept has remained purely theoretical, because isolated single atomic chains of sufficient length have been experimentally unattainable. Here we report on the observation of a length-dependent κ extending over 42.5 µm at room temperature for ultrathin van der Waals crystal NbSe₃ nanowires. We found that κ follows a 1/3 power law with wire length, which provides experimental evidence pointing towards superdiffusive phonon transport. Contrary to the classical size effect due to phonon-boundary scattering, the observed κ shows a 25-fold enhancement as the characteristic size of the nanowires decreases from 26 to 6.8 nm while displaying a normal–superdiffusive transition. Our analysis indicates that these intriguing observations stem from the transport of one-dimensional phonons excited as a result of elastic stiffening with a fivefold enhancement of Young’s modulus. The persistent divergent trend of the observed thermal conductivity with sample length reveals a real possibility of creating novel van der Waals crystal-based thermal superconductors with κ values higher than those of any known materials.