We present a timing study of the young rotation-powered pulsar 0540-69 in the Large Magellanic Cloud , based on 130 kiloseconds of archival ROSAT data spanning a \sim 3 -year period . We use “ f - \dot { f } ” techniques to measure the pulsar frequency as a function of frequency derivative at 17 independent epochs . From these measurements we derive a timing solution with a braking index n = 2.5 ^ { +0.6 } _ { -0.7 } , and we compare this solution to previous timing studies of 0540-69 . Using this frequency-based solution , we create 27 pulse profiles and perform a time-of-arrival ( TOA ) analysis to investigate further the pulsar ’ s timing behavior . While we can successfully fit smooth spin-down models to subsets of the TOAs spanning up to 2 years , we are unable to obtain acceptable phase-coherent fits to the entire 3-year set of TOAs . This behavior provides the first clear evidence for timing noise in 0540-69 . We discuss the implications of these results for understanding previous studies of the timing behavior of 0540-69 .