We observed the nearby, low-density globular cluster M71 (NGC 6838) with the Chandra X-ray Observatory to study its faint X-ray populations. Five X-ray sources were found inside the cluster core radius, including the known eclipsing binary millisecond pulsar (MSP) PSR J1953+1846A. The X-ray light curve of the source coincident with this MSP shows marginal evidence for periodicity at the binary period of 4.2 h. Its hard X-ray spectrum and luminosity resemble those of other eclipsing binary MSPs in 47 Tuc, suggesting a similar shock origin of the X-ray emission. A further 24 X-ray sources were found within the half-mass radius, reaching to a limiting luminosity of 1.5 10^30 erg/s (0.3-8 keV). From a radial distribution analysis, we find that 18+/-6 of these 29 sources are associated with M71, somewhat more than predicted, and that 11+/-6 are background sources, both galactic and extragalactic. M71 appears to have more X-ray sources between L_X=10^30--10^31 erg/s than expected by extrapolating from other studied clusters using either mass or collision frequency. We explore the spectra and variability of these sources, and describe the results of ground-based optical counterpart searches. ; Comment: 36 pages including 7 figures and 8 tables, accepted by The Astrophysical Journal