Oceanic carbonate chemistry during the Cenozoic has affected the climatology, ecology, and marine geology of our planet; yet, we have limited means to know the evolution of that chemistry, due to a lack of preserved and unaltered seawater samples and a continuing paucity of proxies. Modeling is often used to address this problem; here, we offer a simple, data-driven, secular timescale, inverse model for the mean, Cenozoic, carbonate chemistry of the oceans. Inputs for the model include carbonate compensation depth (CCD), CaCO3 burial, seawater temperature, atmospheric CO2 and carbonate ion records, as well as a simple set of original, but justified, assumptions. The model retrodicts the total dissolved inorganic carbon (DIC), carbonate alkalinity (CAlk), and pH of the surface and deep waters of the ocean. The retrodicted DIC and CAlk records do not indicate any unusually elevated values in the early Cenozoic, as found in some past studies. If the CCD record from Lyle et al. (2008) is employed, the changes in DIC and CAlk appear entirely related to changes in the alkalinity input to the pelagic oceans and atmospheric CO2; however, with the CCD from Pälike et al. (2012), the increases in DIC and CAlk during the last 15 Ma reflect the effects of ocean cooling. Using either CCD-record, our model provides consistent retrodictions of the available pH record. Our results are not consistent with many past modeling assumptions, such as constancy of alkalinity in surface waters, or the ratio of shallow and deep carbonate ion concentrations. Finally, we use our results to provide new estimates of atmospheric CO2 based on Boron isotopes and find significantly lower CO2 values in the early Cenozoic than previous values.