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We report the first observation of non-Markovian stochastic resonance (SR), and we discover that memory effects in the nonlinearity extremely enlarge the SR bandwidth. Our experimental system is an oil-filled microcavity which, driven by a continuous wave laser, has memory in its nonlinear optical response. Modulating the cavity length while adding noise to the driving laser, we observe a peak in the transmitted signal-to-noise ratio as a function of the noise variance. Through simulations, we reproduce our observations and extrapolate