There is an increasing demand for designs in aerospace engineering that guarantee baseline performance even in limit states, i.e., outside of nominal operating conditions of vehicles. Typically, the numerical optimization for such risk-averse designs is computationally challenging because in each iteration of the optimization loop the performances of the designs are estimated for the rare events corresponding to the limit states. This work proposes a multifidelity approach to make tractable the optimization of large-scale risk-averse designs that are based on the conditional value-at-risk (CVaR) as the risk measure. The multifidelity method leverages low-cost, low-fidelity models to speed up the CVaR estimation in each iteration of the risk-averse optimization to reduce the runtime compared to traditional Monte Carlo estimators that rely on the high-fidelity models alone. At the same time, the proposed approach makes occasional recourse to the expensive high-fidelity model to guarantee convergence to design points that satisfy the high-fidelity optimality conditions. In numerical experiments with an aerostructural design problem, the multifidelity approach achieves speedups of almost one order of magnitude compared to a traditional single-fidelity method.