Under the background that the high penetration of renewable energy generation, which mainly consists of wind power, will have a significant impact on electric power systems due to the volatility and uncertainty of renewable energy, energy systems with gas–electric coupling and interconnections have been widely studied to accommodate renewable energy generation. This paper proposes a two-stage chance-constrained coordinated operation model of an integrated gas–electric system and fully considers the uncertainty and high penetration of wind power. The Taylor series expansion method is used to linearize the Weymouth gas flow equation of a natural gas system and finally obtains a mixed integer linear programming model. Case studies show the effectiveness of the integrated energy system for peak shaving, valley filling, and promoting wind power accommodation. The proposed model ensures the consumption of wind power generation and also reduces the operation cost by about 0.7%.