  We fit every emission line in the high-resolution Chandra grating spectrum of
zeta Pup with an empirical line profile model that accounts for the effects of
Doppler broadening and attenuation by the bulk wind. For each of sixteen lines
or line complexes that can be reliably measured, we determine a best-fitting
fiducial optical depth, tau_* = kappa*Mdot/4{pi}R_{\ast}v_{\infty}, and place
confidence limits on this parameter. These sixteen lines include seven that
have not previously been reported on in the literature. The extended wavelength
range of these lines allows us to infer, for the first time, a clear increase
in tau_* with line wavelength, as expected from the wavelength increase of
bound-free absorption opacity. The small overall values of tau_*, reflected in
the rather modest asymmetry in the line profiles, can moreover all be fit
simultaneously by simply assuming a moderate mass-loss rate of 3.5 \pm 0.3
\times 10^{-6} Msun/yr, without any need to invoke porosity effects in the
wind. The quoted uncertainty is statistical, but the largest source of
uncertainty in the derived mass-loss rate is due to the uncertainty in the
elemental abundances of zeta Pup, which affects the continuum opacity of the
wind, and which we estimate to be a factor of two. Even so, the mass-loss rate
we find is significantly below the most recent smooth-wind H-alpha mass-loss
rate determinations for zeta Pup, but is in line with newer determinations that
account for small-scale wind clumping. If zeta Pup is representative of other
massive stars, these results will have important implications for stellar and
galactic evolution.
