In this paper, we study in detail the Flight Level Assignment (FLA) problem and its chance-constrained variant. Like FLA, the chance-constrained FLA problem is strongly NP-hard, and solving it exactly is out of reach, even for moderate realistic instances. An efficient heuristic is therefore proposed to deal with the whole problem by solving iteratively the chance-constrained FLA problem separately for each flight level. The approach used to solve the latter problem consists in a constraint generation one which adds iteratively new constraints until reaching the probability threshold for the specific chance-constrained FLA subproblem. An essential aspect of this method is the fast feasibility probability estimation of the chance-constrained constraints of a given solution. Numerical results support our findings.