•A new stochastic model for radiation therapy planning.•A chance-constrained optimization framework to handle setup uncertainties.•Confidence level, the plan quality (robustness and homogeneity) are optimized.•Second order cone constraint counterparts of the model are developed. A stochastic programming framework is proposed for radiation therapy treatment planning. This framework takes into account uncertainty in setting up or positioning patients identically day-to-day during the treatment period. Because uncertainties are unavoidable, constraint violations are tolerated to some degree in practice. Under this assumption, a chance-constrained programming (CCP) framework is developed to handle setup uncertainties in treatment planning. The proposed framework can be employed under different distributional assumptions. The goal of the proposed approach is to maximize both the statistical confidence level of a treatment plan and the homogeneity of the dose distributions. This novel perspective provides a user-centric and personalized optimization model that allows a trade-off between sufficient tumor coverage and sparing healthy tissues under uncertainty. We describe testing of the performance of the proposed CCP models in terms of plan quality, robustness, and homogeneity and confidence level of the constraints using clinical data for a prostate cancer patient. Optimized CCP plans are also compared to plans developed using a deterministic approach that does not take uncertainties into account. Numerical experiments confirmed that the CCP is able to control setup uncertainties in target coverage and sparing of organs-at-risk.