Many previous studies of ζ Puppis (O4I(n)fp) at a variety of wave bands have reported periodic variability for this star. These studies found periods ranging from less than a day up to approximately 5 days, with much recent interest centered on the variability with a period of 1.78 days. We are using time-resolved data for Zeta Puppis from the High Energy Transmission Grating/ACIS-S instrument on the Chandra spacecraft to investigate the variability of this star in the X-ray band. The X-ray data was obtained during the following three intervals: July/August 2018 (464.0 ks), January/February 2010 (74.7 ks), and July/August 2019 (274.4 ks), for a total of 813.1 ks. In this study we concentrate on the temporal behavior of broad-band X-ray spectral regions. These bands are chosen to be wide enough to achieve adequate count rates in the short time intervals required to investigate periodic signals on the time scales described above. We compare this X-ray data with nearly contemporaneous high precision optical space photometric monitoring performed by the BRITE optical satellite array (including some corroborative data from TESS) to explore connections between the star’s photosphere and its strong outflowing wind.