A model for the structure of amorphous molybdenum trisulfide, a-MoS3, has been created using reverse Monte Carlo methods. This model, which consists of chains of MoS6 units sharing three sulfurs with each of its two neighbors and forming alternate long, nonbonded, and short, bonded, Mo-Mo separations, is a good fit to the neutron diffraction data and is chemically and physically realistic. The paper identifies the limitations of previous models based on Mo3 triangular clusters in accounting for the available experimental data.