Several experimental anomalies in neutrino physics may point to the possible existence of one or more additional neutrino species that do not interact weakly, the so-called sterile neutrinos. The third phase of the Borexino experiment (SOX) is devoted to verification of this hypothesis. Within the first stage (CeSOX) the count rate of antineutrino events in the liquid scintillation detector from the artificial source 144Ce–144Pr placed in the special pit beneath the setup will be measured. The smaller antineutrino flux, as compared to the original one, would indicate the presence of oscillations into sterile states. This paper gives a survey of the CeSOX experiment, including the general description, the characterization of the radioactive source and the specific features of its use, the description of the method for data analysis, and the expected results. Depending on the significance of the obtained scientific information, the decision on carrying out the second stage of the SOX experiment with the 51Cr source of electron neutrinos will be made.