The implications of a fundamental asymmetry in the lathe turning process are considered. The asymmetry is the directional dependence of system stiffness that exists at the cutting tool edge. Depending on tool edge displacement, the system stiffness is determined by the workpiece stiffness or the relatively much stiffer tool support structure. A one degree-of-freedom, lumped parameter model with nonlinear stiffness is constructed and subjected to a periodic forcing. Time and frequency domain analysis show that extremely complex dynamic behavior can occur in this simple system.