Let ${τ_n,n≥0}$ be a sequence of measure preserving transformations of a probability space (Ω,Σ,P) into itself and let ${f_n,n≥0}$ be a sequence of elements of $L^2(Ω,Σ,P)$ with $E{f_n}=0$. It is shown that the distribution of $(∑_{i=0}^{n}f_i∘τ_i∘...∘τ_0)(D(∑_{i=0}^nf_i∘τ_i∘...∘τ_0))^{-1}$ tends to the normal distribution N(0,1) as n → ∞.