The field of the extended TeV source HESS J1804 - 216 was serendipitously observed with the Chandra ACIS detector on 2005 May 4 . 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 ( 2005 November 3 ) and Suzaku ( 2006 April 6 ) , is consistent with being a point-like source , with the 0.3–7 keV flux F _ { X } = ( 1.7 \pm 0.2 ) \times 10 ^ { -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 \Gamma \approx 0.45 and hydrogen column density n _ { H } \approx 4 \times 10 ^ { 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 F _ { X } \sim 1 \times 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 ( F _ { X } < 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 \sim 10 pc from the TeV source , still remains a more plausible option .