We fit every emission line in the high-resolution Chandra grating spectrum of ζ Pup with an empirical line profile model that accounts for the effects of Doppler broadening and attenuation by the bulk wind. For each of 16 lines or line complexes that can be reliably measured, we determine a best-fitting fiducial optical depth, τ_∗ ≡ κM/4πR_∗v_∞, and place confidence limits on this parameter. These 16 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 τ_∗ with line wavelength, as expected from the wavelength increase of bound–free absorption opacity. The small overall values of τ ∗, reflected in the rather modest asymmetry in the line profiles, can moreover all be fitted simultaneously by simply assuming a moderate mass-loss rate of 3.5 ± 0.3 × 10^(−6)M_⊙ yr^(−1), 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 ζ Pup, which affects the continuum opacity of the wind, and which we estimate to be a factor of 2. Even so, the mass-loss rate we find is significantly below the most recent smooth-wind Hα mass-loss rate determinations for ζ Pup, but is in line with newer determinations that account for small-scale wind clumping. If ζ Pup is representative of other massive stars, these results will have important implications for stellar and Galactic evolution.