We describe the first X-ray observations of five short orbital period ( P _ { B } < 1 day ) , \gamma -ray emitting , binary millisecond pulsars . Four of these - PSRs J0023+0923 , J1124 - 3653 , J1810+1744 , and J2256 - 1024 - are ‘ black-widow ’ pulsars , with degenerate companions of mass \ll 0.1 ~ { } M _ { \odot } , three of which exhibit radio eclipses . The fifth source , PSR J2215+5135 , is an eclipsing ‘ redback ’ with a near Roche-lobe filling \sim 0.2 solar mass non-degenerate companion . Data were taken using the Chandra X-Ray Observatory and covered a full binary orbit for each pulsar . Two pulsars , PSRs J2215+5135 and J2256 - 1024 , show significant orbital variability while PSR J1124 - 3653 shows marginal orbital variability . The lightcurves for these three pulsars have X-ray flux minima coinciding with the phases of the radio eclipses . This phenomenon is consistent with an intrabinary shock emission interpretation for the X-rays . The other two pulsars , PSRs J0023+0923 and J1810+1744 , are fainter and do not demonstrate variability at a level we can detect in these data . All five spectra are fit with three separate models : a power-law model , a blackbody model , and a combined model with both power-law and blackbody components . The preferred spectral fits yield power-law indices that range from 1.3 to 3.2 and blackbody temperatures in the hundreds of eV . The spectrum for PSR J2215+5135 shows a significant hard X-ray component , with a large number of counts above 2 keV , which is additional evidence for the presence of intrabinary shock emission . This is similar to what has been detected in the low-mass X-ray binary to millisecond pulsar transition object PSR J1023+0038 .