  We report on the first 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 the Kerr rotation and ellipticity noise spectra in the strong
coupling regime. The spin noise spectra clearly show two resonant features: a
conventional magneto-resonant component shifting towards higher frequencies
with magnetic field and an unusual "nonmagnetic" component centered at zero
frequency and getting suppressed with increasing magnetic field. We attribute
the first of them to the Larmor precession of free electron spins, while the
second one being presumably due to hyperfine electron-nuclei spin interactions.
