We construct a new family of chance constrained directional models in stochastic data envelopment analysis, generalizing the deterministic directional models and the chance constrained radial models. We prove that chance constrained directional models define the same concept of stochastic efficiency as the one given by chance constrained radial models and, as a particular case, we obtain a stochastic version of the generalized Farrell measure. Finally, we give some examples of application of chance constrained directional models with stochastic and deterministic directions, showing that inefficiency scores obtained with stochastic directions are less or equal than those obtained considering deterministic directions whose values are the means of the stochastic ones.