Chandra ACIS observed the field of the extended TeV source HESS J1834-087 for 47 ks. A previous XMM-Newton EPIC observation of the same field revealed a point-like source (XMMU J183435.3-084443) and an offset region of faint extended emission. In the low-resolution, binned EPIC images the two appear to be connected. However, the high-resolution Chandra ACIS images do not support the alleged connection. In these images, XMMU J183435.3-084443 is resolved into a point source, CXOU J183434.9-084443 (L_0.5-8 keV_≃ 2.3 x1033 erg/s, for a distance of 4 kpc; photon index Γ ≃ 1.1), and a compact ( ≲ 20'') nebula with an isotropic morphology and a softer spectrum (L_0.5-8 keV_≃ 4.1x1033 erg/s, Γ ≃ 2.7). The nature of the nebula is uncertain. We discuss a dust scattering halo and a pulsar-wind nebula as possible interpretations. Based on our analysis of the X-ray data, we re-evaluate the previously suggested interpretations of HESS J1834-087 and discuss a possible connection to the Fermi Large Area Telescope source 1FGL J1834.3-0842c. We also obtained an upper limit of 3x10–14 erg/cm2/s on the unabsorbed flux of the SGR J1833-0832 (in quiescence), which happened to be in the ACIS field of view.