We derive an area-preserving map from the microscopic model of a nonlinear monatomic chain at a T=0 first-order phase-transition point. The model is useful for describing first-order structural phase transitions and the metal-insulator transition in various condensed-matter systems. We numerically study the nature of the trajectories of this two-parameter map associated with the lattice displacement pattern. The map displays spatial chaotic behavior for various values of the parameters m and \ensuremath{\delta}. The result is interpreted in terms of soliton interaction, soliton pinning, and the metal-insulator transition in these systems.