We describe the dynamics of a stream of equally spaced macroscopic particles in orbit around a central body (e.g. a planet or star). A co-orbital configuration of particles may be subject to gravitational instability, which takes the system to a spreading disordered and collisional state. We detail the linear instability’s mathematical and physical features using the shearing sheet model and subsequently track its non-linear evolution with local N-body simulations. This model provides a convenient tool with which to understand the gravitational and collisional dynamics of narrow belts, such as Saturn’s F ring and the streams of material wrenched from tidally disrupted bodies. In particular, we study the tendency of these systems to form long-lived particle aggregates. Finally, we uncover an unexpected connection between the linear dynamics of the gravitational instability and the magnetorotational instability.