The development of new electrode materials for electrochemical systems for various purposes is a significant and in-demand task of scientific research. Layered transition metal carbides and nitrides, known as MXenes, show great potential for use as electrodes in electrochemical energy storage devices operating in aqueous electrolytes. In this work, a multilayer Ti3C2Tx MXene was obtained from a Ti3AlC2 precursor and studied as the electrode material of a symmetrical supercapacitor with an aqueous LiCl electrolyte. The formation of the MXene structure was confirmed by the data from X-ray phase analysis and scanning electron microscopy. The X-ray diffraction pattern showed the disappearance of the main reflections related to the Ti3AlC2 phase and the shift of the reflection peak (002) from 9.4° to 6.7°, which indicated successful etching of the Al layers from the Ti3AlC2 precursor. At electrolyte concentrations of 1, 5, 10, and 20 M, the supercapacitors demonstrated high specific capacitances of 105, 120, 126, and 151 F·g−1 at a scan rate of 5 mV·s−1. In addition, an increase in the LiCl concentration contributed to the expansion of the potential window from 0.7 to 1 V. It was shown that the contribution of the surface capacitance to the total capacitance of the electrode is about 40% and depends little on the scan rate. In addition, the symmetrical supercapacitor with 5 M electrolyte showed good cyclic stability with capacitance retention of 88% over 10,000 cycles. The parameters of the main components of the physical processes of supercapacitors based on Ti3C2T were determined by the method of impedance spectroscopy.