(abridged) The high-resolution X-ray spectrum of NGC 3783 shows several dozen absorption lines and a few emission lines from the H-like and He-like ions of O, Ne, Mg, Si, and S as well as from Fe XVII - Fe XXIII L-shell transitions. We have reanalyzed the Chandra HETGS spectrum using better flux and wavelength calibrations along with more robust methods. Combining several lines from each element, we clearly demonstrate the existence of the absorption lines and determine they are blueshifted relative to the systemic velocity by -610+/-130 km/s. We find the Ne absorption lines in the High Energy Grating spectrum to be resolved with FWHM=840{+490}{-360} km/s. We have used regions in the spectrum where no lines are expected to determine the X-ray continuum, and we model the absorption and emission lines using photoionized-plasma calculations. The model consists of two absorption components which have an order of magnitude difference in their ionization parameters. The two components are spherically outflowing from the AGN and thus contribute to both the absorption and the emission via P Cygni profiles. The model also clearly requires O VII and O VIII absorption edges. The low-ionization component of our model can plausibly produce UV absorption lines with equivalent widths consistent with those observed from NGC 3783. However, we note that this result is highly sensitive to the unobservable UV-to-X-ray continuum, and the available UV and X-ray observations cannot firmly establish the relationship between the UV and X-ray absorbers. We find good agreement between the Chandra spectrum and simultaneous ASCA and RXTE observations. We set an upper limit on the FWHM of the narrow Fe Kalpha emission line of 3250 km/s. This is consistent with this line originating outside the broad line region, possibly from a torus.
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