The free oscillations of a chain of identical masses connected by identical springs can be very complicated, resembling the chaotic oscillations of nonlinear systems. These oscillations, however, differ in significant ways from chaotic oscillations. They are actually oscillations of a type called almost periodic that are also observed in nonlinear systems. This article solves the equations of motion for longitudinal oscillations in a finite linear chain. The resulting oscillations are discussed and compared with chaotic oscillations. The linear chain can easily be set up as a demonstration.