We present the first phase-coherent measurement of a braking index for the young , energetic rotation-powered pulsar PSR J1846 - 0258 . This 324 ms pulsar is located at the center of the supernova remnant Kes 75 and has a characteristic age of \tau _ { c } = 723 years , a spin-down energy of \dot { E } = 8.3 \times 10 ^ { 36 } erg s ^ { -1 } , and inferred magnetic field of 4.9 \times 10 ^ { 13 } G. Two independent phase-coherent timing solutions are derived which together span 5.5 yr of data obtained with the Rossi X-ray Timing Explorer . In addition , a partially phase-coherent timing analysis confirms the fully phase-coherent result . The measured value of the braking index , n = 2.65 \pm 0.01 , is significantly less than 3 , the value expected from magnetic dipole radiation , implying another physical process must contribute to the pulsar ’ s rotational evolution . Assuming the braking index has been constant since birth , we place an upper limit on the spin-down age of PSR J1846 - 0258 of 884 yr , the smallest age estimate of any rotation-powered pulsar .