the wiener chaos is a natural orthogonal decomposition of the $l^2$ space of a brownian motion, naturally associated to stochastic integration theory; the orders of chaos are given by the range of multiple wiener-ito integrals. in 2006, nualart and collaborators proved a remarkable central limit theorem in the context of the chaos. if $x_k$ is a sequence of $n$th wiener-ito integrals (in the $n$th chaos), then necessary and sufficient conditions that $x_k$ converge weakly to a normal law are that its (second and) fourth moments converge -- all other moments are controlled by these. in this lecture, i will discuss recent joint work with roland speicher in which we prove an analogous theorem for the empirical eigenvalue laws of high-dimensional random matrices.