Optically levitated micro- and nanoparticles offer an ideal playground for investigating photon-phonon interactions over macroscopic distances. Here we report the observation of long-range optical binding of multiple levitated microparticles, mediated by intermodal scattering and interference inside the evacuated core of a hollow-core photonic crystal fibre (HC-PCF). Three polystyrene particles with a diameter of 1 µm are stably bound together with an inter-particle distance of ~40 μm, or 50 times longer than the wavelength of the trapping laser. The levitated bound-particle array can be translated to-and-fro over centimetre distances along the fibre. When evacuated to a gas pressure of 6 mbar, the collective mechanical modes of the bound-particle array are able to be observed. The measured inter-particle distance at equilibrium and mechanical eigenfrequencies are supported by a novel analytical formalism modelling the dynamics of the binding process. The HC-PCF system offers a unique platform for investigating the rich optomechanical dynamics of arrays of levitated particles in a well-isolated and protected environment.