We explore theoretically and experimentally the first creation of extended longitudinally optically bound chains of microparticles in one dimension. We use the geometry of two counter-propagating "non-diffracting" light fields, so termed Bessel beams. Such beams suppressed the influence of the axial intensity profiles of the illuminating beams on the self-organisation process which then depended critically upon the inter-beads interactions. Beam homogeneity and extended propagation allowed the creation of 200μm long chains of organised micro-particles and the first observation of multi-stability: short range multistability within a single chain and a long-range multi-stability between several distinct chains. Our observations are supported by theoretical results of the coupled dipole method.