We describe the first X-ray observations of binary millisecond pulsars PSR J0023+0923, J1810+1744, J2215+5135, and J2256-1024. All are Fermi gamma-ray sources and three are 'black-widow' pulsars, with companions of mass < 0.1 M âŠ™. Data were taken using the Chandra X-Ray Observatory and covered a full binary orbit for each pulsar. PSRs J2215+5135 and J2256-1024, show significant orbital variability and X-ray flux minima coinciding with eclipses seen at radio wavelengths. This is consistent with intrabinary shock emission characteristic of black-widow pulsars. The other two pulsars, PSRs J0023+0923 and J1810+1744, do not demonstrate significant variability, but are fainter than the other two sources. Spectral fits yield power-law indices that range from 1.4 to 2.3 and blackbody temperatures in the hundreds of eV. The spectrum for PSR J2215+5135 shows a significant hard X-ray component (41% of counts are above 2 keV), which is additional evidence for the presence of intrabinary shock emission.