Electrochemical impedance spectroscopy was used to investigate the chemical capacitance of La0.6Sr0.4CoO3−δ (LSC) thin-film electrodes under anodic polarization (i.e., in the electrolysis mode). For this purpose, electrodes with different microstructures were prepared via pulsed-laser deposition. Analysis of dense electrodes and electrodes with open porosity revealed decreasing chemical capacitances with increasing anodic overpotentials, as expected from defect chemical considerations. However, extremely high chemical capacitance peaks with values in the range of 104 F/cm3 at overpotentials of >140 mV were obtained after annealing for several hours in synthetic air and/or after applying high anodic bias voltages of >750 mV. From the results of several surface analysis techniques and transmission electron microscopy, it is concluded that closed pores develop upon both of these treatments: (i) During annealing, initially open pores get closed by SrSO4, which forms due to strontium segregation in measurement gases with minute traces of sulfur. (ii) The bias treatment causes mechanical failure and morphological changes including closed pores in the bulk of dense films. Under anodic polarization, high-pressure oxygen accumulates in those closed pores, and this causes the capacitance peak. Model calculations based on a real-gas equation allow us to properly predict the experimentally obtained capacitance increase.