Previous X-ray and ultraviolet spectroscopy suggested that the Fe/O abundance ratio in NGC 1068 may be abnormally high. We have tested this suggestion by measuring and modeling the ASCA spectrum of NGC 1068. We have measured some 15 X-ray lines, to an accuracy better than a factor of 2, and modeled the continuum in two different ways. The first assumes that the hard X-ray continuum is the reflection of the nuclear source by two extended, photoionized gas components; a warm (T ~ 1.5 × 105 K) gas and a hot (T ~ 3 × 106 K) gas. All the observed emission lines are produced in this gas, and there is an additional, extended 0.6-3 keV pure continuum component. The model is similar to the one proposed by Marshall et al. (1993). The second model is a combination of a hard reflected continuum with a soft thermal plasma component. The calculations show that the emission lines in the photoionized gas model are in very good agreement with the observed ones assuming solar metallicity for all elements except for iron, which is more than twice solar, and oxygen, which is less than 0.25 solar. Models with solar oxygen are possible if the 0.5-1 keV continuum is weaker, but they do not explain the magnesium and silicon lines. The thermal model fit requires extremely low metallicity (0.04 solar) for all elements. We discuss these findings and compare them with the ASCA spectra of recently observed starburst galaxies. We argue that the apparent low metallicity of starburst galaxies, as well as of the extended nuclear source in NGC 1068, are inconsistent with galaxy chemical evolution. The explanation for this apparent anomaly is still unknown and may involve nonthermal continuum mechanisms and, in some cases, depletion onto grains. Given the strong H-like and He-like lines, as well as the prominent Fe L emission features, the origin of the soft X-ray lines in this source is more likely photoionized gas. We compare our model with the recent Iwasawa, Fabian, & Matt (1997) paper. We also show that fluorescence lines of low-Z elements in AGNs are likely to be stronger than previously assumed.