Operators acting on a collection of two-level quantum-mechanical systems can be represented by quantum circuits. This work presents a new universal quantum circuit capable of implementing any unitary operator. The circuit has a top-down structure, and the parameters for individual unitaries can be computed using standard matrix analysis algorithms. The number of generated controlled-not gates is no more than half the number of matrix coefficients. Moreover, a theoretical lower bound shows that this new universal circuit may not be improved by more than a factor of two. The circuit adapts well to architectures in which only nearest-neighbor interactions are possible, i.e., spin chains.