We report here the results of the first Chandra X-Ray Observatory observations of the globular cluster M28 ( NGC 6626 ) . We detect 46 X-ray sources of which 12 lie within one core radius of the center . We show that the apparently extended X-ray core emission seen with the ROSAT HRI is due to the superposition of multiple discrete sources for which we determine the X-ray luminosity function down to a limit of about 6 \times 10 ^ { 30 } erg s ^ { -1 } . We measure the radial distribution of the X-ray sources and fit it to a King profile finding a core radius of r _ { c,x } \approx 11 \arcsec . We measure for the first time the unconfused phase-averaged X-ray spectrum of the 3.05-ms pulsar B1821 - 24 and find it is best described by a power law with photon index \Gamma \simeq 1.2 . We find marginal evidence of an emission line centered at 3.3 keV in the pulsar spectrum , which could be interpreted as cyclotron emission from a corona above the pulsar ’ s polar cap if the the magnetic field is strongly different from a centered dipole . The unabsorbed pulsar flux in the 0.5–8.0 keV band is \approx 3.5 \times 10 ^ { -13 } { ergs s } ^ { -1 } { cm } ^ { -2 } . We present spectral analyses of the 5 brightest unidentified sources . Based on the spectral parameters of the brightest of these sources , we suggest that it is a transiently accreting neutron star in a low-mass X-ray binary , in quiescence . Fitting its spectrum with a hydrogen neutron star atmosphere model yields the effective temperature T _ { eff } ^ { \infty } = 90 ^ { +30 } _ { -10 } eV and the radius R _ { NS } ^ { \infty } = 14.5 ^ { +6.9 } _ { -3.8 } km . In addition to the resolved sources , we detect fainter , unresolved X-ray emission from the central core . Using the Chandra -derived positions , we also report on the result of searching archival Hubble Space Telescope data for possible optical counterparts .