We give an algorithm that learns arbitrary Boolean functions of $k$ arbitrary halfspaces over $\R^n$, in the challenging distribution-free Probably Approximately Correct (PAC) learning model, running in time $2^{\sqrt{n} \cdot (\log n)^{O(k)}}.$ This is the first algorithm that can PAC learn even intersections of two halfspaces in time $2^{o(n)}.$