The field of the extended TeV source HESS J1804À216 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 J1804À216. The brightest of these objects, CXOU J180432.4À214009, which has been also detected with Swift (2005 November 3) and Suzaku (2006 April 6), is consistent with being a pointlike source, with the 0.3Y7 keV flux F X ¼ (1:7 AE 0:2) ; 10 À13 ergs s À1 cm À2 . Its hard and strongly absorbed spectrum can be fitted by the absorbed power-law model with the best-fit photon index À % 0:45 and hydrogen column density n H % 4 ; 10 22 cm À2 , both with large uncertainties due to the strong correlation between these parameters. A search for pulsations resulted in a 106 s period candidate, which has a low significance of 97.9%, however. We found no infrared-optical counterparts for this source. The second brightest source, CXOU J180441.9À214224, which has been detected with Suzaku, is either extended or multiple, with the flux F X $ 1 ; 10 À13 ergs cm À2 s À1 . 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 ; 10 À14 ergs cm À2