The advantages of compressed air energy storage (CAES) have been demonstrated by the trigeneration system with the characteristic of high penetration of renewable energy. However, since the irreversible loss of compression heat occurs during the overall operation processes of CAES, the development of CAES with high energy efficiency has been hindered by the conventional conversion pathway of compression heat. Therefore, a trigeneration system integrated with compressed air and chemical energy storage is proposed in this study to improve energy utilization efficiency. The compression heat is converted into H2 and CO via the endothermic methanol decomposition reaction to improve its energy level during the charging process, and then the syngas production can be used for air preheating during the discharging process. The parametric analysis is first performed to investigate the technical and economic feasibility of the system. Subsequently, the multi-objective optimization is conducted to identify the tradeoffs in the thermo-economic performance of the system and acquire the optimal values of operating parameters. Notably, the proposed system with a computed exergy efficiency of 43.31% and levelized cost of energy (LCOE) of 97.53 $/MWh is selected as the most compromise solution by the decision maker of Technique for Order Preference by Similarity to an Ideal Solution among the Pareto optimum fronts, which are 8.47% higher than the exergy efficiency and 7.39 $/MWh lower than the LCOE under the design conditions.