  We have obtained and analyzed Chandra ACIS-S observations of the strongly
accreting classical T Tauri star DG Tau. Our principal goals are to map the
immediate environment of the star to characterize possible extended X-rays
formed in the jet, and to re-visit the anomalous, doubly absorbed X-ray
spectrum of DG Tau itself. We combine our new ACIS-S data with a data set
previously obtained. The data are superimposed to obtain flux and hardness
images. Separate X-ray spectra are extracted for DG Tau and areas outside its
point spread function. We detect a prominent X-ray jet at a position angle of
PA ~225 deg (tentatively suggested by Guedel et al. 2005), coincident with the
optical jet axis. We also identify a counter jet at PA = 45 deg. The X-ray jets
are detected out to a distance of ~5" from the star, their sources being
extended at the ACIS-S resolution. The jet spectra are soft, with a best-fit
electron temperature of 3.4 MK. We find evidence for excess absorption of the
counter jet. The spectrum of the DG Tau point source shows two components with
largely different temperatures and absorption column densities. The similar
temperatures and small absorbing gas columns of the jet sources and the soft
component of the "stellar" source suggest that these sources are related,
produced either by shocks or by magnetic heating in the jets. Cooling estimates
suggest that the pressure in the hot gas contributes to jet expansion. The hard
"stellar" component, on the other hand, is associated with a stellar corona or
magnetosphere. The excessive photoelectric absorption of this component
suggests the presence of dust-depleted accretion streams above coronal magnetic
fields.
