We extend a sociophysics model of two-group conflict dynamics to three groups. The model with attractors and chaos is proposed as a tool for exploring and managing intractable conflicts. It can be used to generate scenarios of trajectories and outcomes. We use mean-field theory for long-range interactions to study the time dependence of the three grousp' mean attitudes. We find that at some intermediate temperatures the group mean attitudes oscillate in time. Independent of initial conditions, trajectories converge overtime to an attractor in the three-dimensional space of mean attitudes. We use Monte Carlo simulations to explore short-range group interactions and find chaotic unpredictable time variation of attitudes at high temperatures. For illustrative purposes we apply the model to the Bosnia and Herze-govina conflict.