  We report on archival Hubble Space Telescope (HST) observations of the
globular cluster M71 (NGC 6838). These observations, covering the core of the
globular cluster, were performed by the Advanced Camera for Surveys (ACS) and
the Wide Field Planetary Camera 2 (WFPC2). Inside the half-mass radius (r_h =
1.65') of M71, we find 33 candidate optical counterparts to 25 out of 29
Chandra X-ray sources while outside the half-mass radius, 6 possible optical
counterparts to 4 X-ray sources are found. Based on the X-ray and optical
properties of the identifications, we find 1 certain and 7 candidate
cataclysmic variables (CVs). We also classify 2 and 12 X-ray sources as certain
and potential chromospherically active binaries (ABs), respectively. The only
star in the error circle of the known millisecond pulsar (MSP) is inconsistent
with being the optical counterpart. The number of X-ray faint sources with
L_x>4x10^{30} ergs/s (0.5-6.0 keV) found in M71 is higher than extrapolations
from other clusters on the basis of either collision frequency or mass. Since
the core density of M71 is relatively low, we suggest that those CVs and ABs
are primordial in origin.
