  We investigate a nonlinear dynamical system which ``remembers'' preselected
values of a system parameter. The deterministic version of the system can
encode many parameter values during a transient period, but in the limit of
long times, almost all of them are forgotten. Here we show that a certain type
of stochastic noise can stabilize multiple memories, enabling many parameter
values to be encoded permanently. We present analytic results that provide
insight both into the memory formation and into the noise-induced memory
stabilization. The relevance of our results to experiments on the
charge-density wave material $NbSe_3$ is discussed.
