Analysis of very deep, high resolution X-ray spectroscopy of the early O supergiant zeta Pup, acquired by Chandra in 2018-9, is presented. The cumulative spectrum has an exposure time of 820 kiloseconds (almost 10 days) and covers the wavelength range 3-20 Å. The X-ray broad-band light curve displays significant variability with one clear period, 1.78d, which has been previously detected in optical. The correlation with optical and UV data is discussed, notably in the context of CIRs and (possibly magnetic?) spots on the stellar surface with at least one stable period. The possible correlation of periods with optical and UV data is discussed. The X-ray spectrum is divided into several wavelength bands which are explored for variability. These divisions allow construction of light curves for hard, medium, and soft bands individually (which allows calculations of time-dependent hardness ratios), along with independently investigating the temporal behavior of strong X-ray emission lines. New constraints on the structure of stellar winds for the most massive stars are discussed.