  Using the combined spectral and spatial resolving power of the Low Energy
Transmission Grating (LETGS) on board Chandra, we obtain separate spectra from
the bright central source of NGC 1068 (Primary region), and from a fainter
bright spot 4" to the NE (Secondary region). Both spectra are dominated by line
emission from H- and He-like ions of C through S, and from Fe L-shell ions, but
also include narrow radiative recombination continua, indicating that most of
the soft X-ray emission arises in low-temperature (kT few eV) photoionized
plasma. We confirm the conclusions of Kinkhabwala et al. (2002), based on
XMM-Newton RGS observations, that the entire nuclear spectrum can be explained
by recombination/radiative cascade following photoionization, and radiative
decay following photoexcitation, with no evidence for hot, collisionally
ionized plasma. In addition, this model also provides an excellent fit to the
spectrum of the Secondary region, albeit with radial column densities a factor
of three lower, as would be expected given its distance from the source of the
ionizing continuum. The remarkable overlap and kinematical agreement of the
optical and X-ray line emission, coupled with the need for a distribution of
ionization parameter to explain the X-ray spectra, collectively imply the
presence of a distribution of densities (over a few orders of magnitude) at
each radius in the ionization cone. Relative abundances of all elements are
consistent with Solar abundance, except for N, which is 2-3 times Solar. The
long wavelength spectrum beyond 30 A is rich of L-shell transitions of Mg, Si,
S, and Ar, and M-shell transitions of Fe. The velocity dispersion decreases
with increasing ionization parameter, as deduced from these long wavelength
lines and the Fe-L shell lines.
