As a type of renewable energy, wind energy is integrated into the power system with more and more penetration levels. It is challenging for the power system operators (PSOs) to cope with the uncertainty and variation of the wind power and its forecasts. A chance-constrained economic dispatch (ED) model for the wind-thermal-energy storage system (WTESS) is developed in this paper. An optimization model with the wind power and the energy storage system (ESS) is first established with the consideration of both the economic benefits of the system and less wind curtailments. The original wind power generation is processed by the ESS to obtain the final wind power output generation (FWPG). A Gaussian mixture model (GMM) distribution is adopted to characterize the probabilistic and cumulative distribution functions with an analytical expression. Then, a chance-constrained ED model integrated by the wind-energy storage system (W-ESS) is developed by considering both the overestimation costs and the underestimation costs of the system and solved by the sequential linear programming method. Numerical simulation results using the wind power data in four wind farms are performed on the developed ED model with the IEEE 30-bus system. It is verified that the developed ED model is effective to integrate the uncertain and variable wind power. The GMM distribution could accurately fit the actual distribution of the final wind power output, and the ESS could help effectively decrease the operation costs.