The output of a mode-locked femtosecond laser is used for precision single-photon spectroscopy of 133Cs in an atomic beam. By changing the laser's repetition rate, the cesium D1 (6s 2S(1/2)-->6p 2P(1/2)) and D2 (6s 2S(1/2)-->6p 2P(3/2)) transitions are detected and the optical frequencies are measured with accuracy similar to that obtained with a cw laser. Control of the femtosecond laser repetition rate by use of the atomic fluorescence is also implemented, thus realizing a simple cesium optical clock.