The amplitude of the parity-nonconserving transition between the 6S and 7S states of cesium was precisely measured with the use of a spin-polarized atomic beam. This measurement gives Im(E1(pnc))/beta = -1.5935(56) millivolts per centimeter and provides an improved test of the standard model at low energy, including a value for the S parameter of -1.3(3)(exp)(11)(theory). The nuclear spin-dependent contribution was 0.077(11) millivolts per centimeter; this contribution is a manifestation of parity violation in atomic nuclei and is a measurement of the long-sought anapole moment.