We report a single-chain magnet (SCM) made of a terbium(III) building block and a nitronyl-nitroxide radical (NIT) functionalized with an aliphatic chain. This substitution is targeted to induce a long-range distortion of the polymeric chain and accordingly it gives rise to chains that are curled with almost 20 nm helical pitch. They self-organize as a chiral tubular superstructure made of 11 chains wound around each other. The supramolecular tubes have a 4.5 nm internal diameter. Overall, this forms a porous chiral network with almost 44 % porosity. Ab initio calculations highlight that each TbIII ion possesses high magnetic anisotropy. Indeed, notwithstanding the supramolecular arrangement each chain behaves as a SCM. Magnetic relaxation with both finite and infinite-size regimes is observed and confirms the validity of the Ising approximation. This is associated with quite strong coercive field and magnetic remanence (Hc =2400 Oe MR =2.09 μB at 0.5 K) for this class of compounds.