We report on an experimental observation of spin noise in a single semiconductor quantum well embedded into a microcavity. The great cavity-enhanced sensitivity to fluctuations of optical anisotropy has allowed us to measure theKerr rotation and ellipticity noise spectra in the strong-coupling regime. The spin noise spectra clearly show two resonant features: a conventionalmagnetoresonant component shifting towards higher frequencies with a magnetic field and an unusual “nonmagnetic” component centered at zero frequency and getting suppressed with an increasing magnetic field. We attribute the first of them to the Larmor precession of free electron spins, whereas, the second one is presumably due to hyperfine electron-nuclei spin interactions.