  We analyze from the viewpoint of an abstract Markov operator recent results
by Nualart and Peccati, and Nourdin and Peccati, on the fourth moment as a
condition on a Wiener chaos to have a distribution close to Gaussian. In
particular, we are led to introduce a notion of chaos associated to a Markov
operator through its iterated gradients and present conditions on the (pure)
point spectrum for a sequence of chaos eigenfunctions to converge to a Gaussian
distribution. Convergence to gamma distributions may be examined similarly.
