Future Grids will integrate time-intermittent renewables and demand response whose fluctuating outputs will create perturbations requiring probabilistic measures of resilience. When smart but uncontrollable resources fluctuate, Optimum Power Flow (OPF), routinely used by the electric power industry to dispatch controllable generation over control areas of transmission networks, can result in higher risks. Our Chance Constrained (CC) OPF corrects the problem and mitigates dangerous fluctuations with minimal changes in the current operational procedure. Assuming availability of a reliable forecast parameterizing the distribution function of the uncertain resources, our CC-OPF satisfies all the constraints with high probability while simultaneously minimizing the cost of economic dispatch. For linear (DC) modeling of power flows, and parametrization of the uncertainty through Gaussian distribution functions the CC-OPF turns into convex (conic) optimization, which allows efficient and scalable cutting-plane implementation. When estimates of the Gaussian parameters are imprecise we robustify CC-OPF deriving its data ambiguous and still scalable implementation.