The emergence of connected vehicle (CV) technology has prompted research on leveraging real-time CV data for more effective traffic signal control. However, existing studies tend to i) utilize traffic parameters estimated by past CVs for signal optimization, resulting in a lag in signal provision, and ii) ignore the impact of parameter estimation/prediction errors inevitably introduced by the limited availability of CV data, which can significantly degrade the performance of signal control models that rely on these parameters. To fill these research gaps, this study proposes a CV-based contextual stochastic optimization (CV-CSO) model for real-time traffic signal timing, which combines a rolling-horizon optimization scheme with a sequential learning and optimization (SLO) paradigm to incorporate updated CV observations and explicitly handle potential parameter errors. The rolling-horizon optimization scheme optimizes two consecutive future cycles at each decision step and re-optimizes every half-cycle. The SLO paradigm, on the other hand, comprises two components: a Gaussian process regression that predicts the conditional distribution of the arrival rate and a contextual two-stage stochastic optimization model that handles the uncertainty of the arrival rate. Evaluation results demonstrate that the proposed CV-CSO model and its simplified deterministic model (denoted as CV-DO) outperform the traditional actuated control approach in terms of average vehicle delay, even with low-penetration-rate CVs. Notably, the consideration of arrival rate uncertainties in the CV-CSO model yields superior performance compared to the deterministic CV-DO model in various scenarios.