We report the discovery of pulsed X-ray emission from the compact object CXOU J112439.1-591620 within the supernova remnant (SNR) G292.0+1.8 using the High Resolution Camera on the Chandra X-ray Observatory. The X-ray period (P=0.13530915 s) is consistent with extrapolation of the radio pulse period of PSR J1124-5916 for a spindown rate of dP/dt=7.6E-13 s/s. The X-ray pulse is single peaked and broad with a FWHM width of 0.23P (83 degrees). The pulse-averaged X-ray spectral properties of the pulsar are well described by a featureless power law model with an absorbing column density, N_H= 3.1E21 atoms/cm^2; photon index, gamma = 1.6; and unabsorbed 0.3-10 keV band luminosity, L_X = 7.2E32 erg/s. We plausibly identify the location of the pulsars termination shock. Pressure balance between the pulsar wind and the larger synchrotron nebula, as well as lifetime issues for the X-ray-emitting electrons, argues for a particle- dominated PWN that is far from the minimum energy condition. Upper limits on the surface temperature of the neutron star are at, or slightly below, values expected from ``standard cooling curves. There is no optical counterpart to the new pulsar; its optical luminosity is at least a factor of 5 below that of the Crab pulsar.
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