We use ab initio molecular dynamics simulations based on density-functional theory and quantum-chemistry calculations on molecular clusters to examine the structure of liquid AlCl3. In the past, conflicting descriptions of the short-range-order in molten AlCl3, based on either edge-sharing dimers or corner-sharing oligomers, have been proposed. This liquid also poses a simulation challenge, due to the possibility of ring-like trimers which can be metastable on the order of > 10 ps. Simulations which begin with monomers, either random or ordered, appear to be able to produce proper ratios of ring-trimer to dimer-plus-tail molecular structures without the need to achieve long-time scale chemical equilibrium. Single-molecule calculations lend further support to the conclusion that the liquid is composed largely of edge-sharing dimers.