This paper considers a Disassembly Line Balancing Problem (DLBP) under uncertainty. Disassembly task times are assumed to be random variables with known probability distributions. To deal with this uncertainty, a stochastic program is developed. It both chooses the best disassembly alternative for an end of life product and assigns the corresponding disassembly tasks to the workstations of the line with the aim to minimize the line cost. The latter includes the operation costs for workstations as well as penalty costs generated by the cycle time constraint violations. AND/OR precedence constraints among tasks are observed. A proposed solution algorithm is capable of providing high quality solutions even for large scale problem instances. It integrates Monte Carlo sampling techniques with the L-shaped algorithm.