  The field of the extended TeV source HESS J1804-216 was serendipitously
observed with the Chandra ACIS detector. The data reveal several X-ray sources
within the bright part of HESS J1804-216. The brightest of these objects, CXOU
J180432.4-214009, which has been also detected with Swift and Suzaku, is
consistent with being a point-like source, with the 0.3-7 keV flux of
(1.7\pm0.2)\times10^{-13} ergs s^{-1} cm^{-2}. Its hard and strongly absorbed
spectrum can be fitted by the absorbed power-law model with the best-fit photon
index of 0.45 and hydrogen column density of 4\times10^{22} cm^{-2}, both with
large uncertainties due to the strong correlation between these parameters. A
search for pulsations resulted in a 106 s period candidate, which however has a
low significance of 97.9%. We found no infrared-optical counterparts for this
source. The second brightest source, CXOU J180441.9-214224, which has been
detected with Suzaku, is either extended or multiple, with the flux of about
10^{-13} ergs cm^{-2} s^{-1}. We found a nearby M dwarf within the X-ray source
extension, which could contribute a fraction of the observed X-ray flux. The
remaining sources are very faint (<3\times 10^{-14} ergs cm^{-2} s^{-1}), and
at least some of them are likely associated with nearby stars. Although one or
both of the two brighter X-ray sources could be faint accreting binaries or
remote pulsars with pulsar wind nebulae (hence possible TeV sources), their
relation to HESS J1804-216 remains elusive. The possibility that HESS J1804-216
is powered by the relativistic wind from the young pulsar B1800-21, located at
a distance of about 10 pc from the TeV source, still remains a more plausible
option.
