Carbon nanotubes (CNTs), with their unique quasi-one-dimensional structure and robust hexagonal covalent bonding, showcase exceptional carrier mobility and conductivity due to minimal scattering events. Despite this, common defects like voids and impurities in CNTs significantly impact electronic properties by increasing scattering. However, the dynamics may differ fundamentally for CNTs carrying bosons (e.g., phonons). In this letter, we devised a phononic “CNT” for surface acoustic waves (SAWs), utilizing a honeycomb lattice of mechanical resonators on a solid cylinder, mirroring the electronic bands of armchair CNTs—symmetric and gapless. This phononic system, unlike its electronic counterparts, permits the independent excitation of eigenmode. Through mode selection, we achieve symmetry-breaking in its band structure, resulting in two separate chiral SAW bands. This novel chiral anomaly, inherent to the boson system, persists irrespective of excitation. Experimental evidence shows robust antiscattering and defect immunity in SAW transmission. This study broadens the horizon in CNTs, promising advancements in artificial crystals harnessing mechanical and electromagnetic waves. Moreover, the attributes of phononic CNTs—i.e., broadband, robust, efficient, linear dispersion, and high-flux wave transmission—herald new possibilities in phonon-based technologies for information processing, sensing, energy harvesting, and neural networking.