A hierarchically organized Co3O4 nanopowder was obtained via programmed chemical precipitation, exhibiting several levels of microstructural self-organization: the initial particles are 40 ± 5 nm in size (average CSR size is 32 ± 3 nm), have a somewhat distorted rounded shape and are combined into curved chains, which, in turn, form flat agglomerates of approximately 350 ± 50 nm in diameter. The thermal behavior of the semiproduct (β-Co(OH)2) was studied by means of a synchronous thermal analysis (TGA/DSC). The obtained powders were examined by X-ray diffraction analysis (XRD) and Fourier-transform infrared spectroscopy (FTIR). Nanopowder of cobalt(II,III) oxide was employed as a functional ink component for the microplotter printing of the corresponding film on the chip surface, and the preservation of the material’s crystal structure was confirmed by XRD and Raman spectroscopy (RS). The microstructural features of the resulting film were analyzed by scanning electron microscopy (SEM) and atomic force microscopy (AFM). Kelvin probe force microscopy (KPFM) was utilized to estimate the work function of the material surface, and the scanning capacitance microscopy (SCM) data indicated the intergranular conductivity type. The results of the conducted chemosensor measurements demonstrate that the printed Co3O4 film exhibits hydrogen sulfide selectivity and a rather high sensory response (S = 131% for 100 ppm) to this analyte at an operating temperature of 250 °C. The dependence of the sensor response value and time when detecting H2S in the concentration range of 4–200 ppm was determined and the high reproducibility of the signal was demonstrated.