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We present high-resolution X-ray images taken with the Chandra X-rayObservatory of the field that contains the unidentified TeV gamma-ray sourceHESS J1804-216. A total of eleven discrete sources were detected with aposteriori significance of > 5 sigma over the entire field of view. Among them,only one, designated as CXOU J180351.4-213707, is significantly extended. Thesource is about 40" away from the radio pulsar PSR J1803-2137, which was thetarget of the Chandra observation but was not detected in X-rays. A naturalquestion is whether the two sources are physically related. While it isconceivable that CXOU J180351.4-213707 could be associated with a previouslyunknown supernova remnant (SNR), in which the pulsar was born, it seems equallyplausible that it might be a pulsar wind nebula (PWN) that is powered by adifferent pulsar whose emission is beamed away from us. In either case, weargue that CXOU J180351.4-213707 is likely the X-ray counterpart of HESSJ1804-216, based on the fact that the Galactic TeV gamma-ray sources arepredominantly SNRs or PWNe. The X-ray spectrum of the source can be fitted wellwith a power law, although the model is not well constrained due to largestatistical uncertainties. The spectrum seems to be very hard, with thebest-fit photon index about 1.2. Under the assumption that CXOUJ180351.4-213707 is the X-ray counterpart of HESS J1804-216, we attempted tomodel the X-ray and TeV emission as synchrotron and inverse Compton scatteredradiation from relativistic electrons. We briefly discuss the results.Comment: 14 pages including 4 figures. Accepted by ApJ Letters. Corrected a  typo in the value of N_

Chandra View of the Unidentified TeV Gamma-Ray Source HESS J1804-216