Electricity markets contain many uncertainties such as changes in generation and demand levels. Especially with increasing integration of wind power, uncertainties in generation availability have increased. This increases the network access risk for generators. Therefore, the need for a reliability mechanism for generators has emerged. Firm transmission access is a transmission reliability mechanism for generators. In order to find the optimal firm access for generators, network reliability studies under uncertainties need to be conducted by the network operator. In the literature, deterministic methods have been widely used. Deterministic approaches might lead to sub-optimal results, since they do not consider the likelihood of scenarios. Therefore, this paper proposes a probabilistic approach to estimate the optimal firm transmission access in the presence of wind power and demand uncertainties, through a chance-constrained optimisation model.