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We present a new phase-coherent timing analysis for the young, energetic pulsar PSR B0540-69 using 7.6 yr of data from the Rossi X-Ray Timing Explorer. We measure the braking index, n=2.140±0.009, and discuss our measurement in the context of other discordant values reported in the literature. We present an improved source position from the phase-coherent timing of the pulsar, to our knowledge, the first of its kind from X-ray pulsar timing. In addition, we detect evidence for a glitch that had been previously reported but later disputed. The glitch occurred at MJD 51,335±12 with Δν/ν=(1.4±0.2)x10^–9 and Δν{dot}/ν{dot}=(1.33±0.02)x10^–4. We calculate that the glitch activity parameter for PSR B0540-69 is 2 orders of magnitude smaller than that of the Crab pulsar, which otherwise has very similar properties. This suggests that neutron stars of similar apparent ages, rotation properties, and inferred dipolar B fields can have significantly different internal properties.