We give a simple proof of Curtis' theorem: if A• is a k-connected free simplicial abelian group, then Ln(A•) is a k + ⌈ log₂ n⌉-connected simplicial abelian group, where Ln is the n-th Lie power functor. In the proof we do not use Curtis' decomposition of Lie powers. Instead we use the Chevalley Eilenberg complex for the free Lie algebra.