We report the first detection of pulsed X-ray emission from the young, energetic radio and gamma-ray pulsar PSR B1706-44. We find a periodic signal at a frequency of f = 9.7588088+/-0.0000026 Hz (at epoch 51585.34104 MJD), consistent with the radio ephemeris, using data obtained with the High Resolution Camera on board the Chandra X-Ray Observatory. The probability that this detection is a chance occurrence is 3.5 x 10(-5) as judged by the Rayleigh test. The folded light curve has a broad, single-peaked profile with a pulsed fraction of 23%+/-6%. This result is consistent with a ROSAT PSPC upper limit of less than 18% after allowing for the ability of Chandra to resolve the pulsar from a surrounding synchrotron nebula. We also fitted Chandra spectroscopic data on PSR B1706-44, which require at least two components, e. g., a blackbody of T-infinity = 1.66(-0.15)(+0.17) x 10(6) K and a power law of Gamma = 2.0+/-0.5. The blackbody radius at the nominal 2.5 kpc distance is only R-infinity - 3.6+/-0.9 km, indicating either a hot region on a cooler surface or the need for a realistic atmosphere model that would allow a lower temperature and larger area. Because the power-law and blackbody spectra each contribute more than 23% of the observed flux, it is not possible to decide which component is responsible for the modulation in the spectrally unresolved light curve.