This paper develops a robust chance-constrained model for handling the uncertainties of generation and consumption in multi-carrier energy hubs. The proposed model incorporates corresponding loading factors for each type of electrical, heating, and cooling loads. This is done to assess the maximum loadability of the whole system. In this respect, the chance-constrained approach is implemented for the feasibility assessment of the operation problem with uncertainties. The uncertainties which are assumed here include the forecast errors of electrical, heating, and cooling load demands, and the volatile solar power generation. The overall problem formulation is developed in the mixed-integer linear programming (MILP) framework. The standard chance-constrained approach is converted to a deterministic optimization model by utilizing the Big M method. The main objective of the proposed model is to maximize the loadability index with uncertainties while addressing the permissible risk index of the decision-maker. The studied energy hub comprises electrical, heating, and cooling loads, and the energy flow technique is adopted in this paper to model the load balance equations. The simulation results are presented for different scenarios while addressing features of the proposed model for the summer and winter seasons. Furthermore, the developed model is evaluated for different scenarios and a comparison is made with the information-gap decision theory (IGDT) method.