The assembly line balancing problems have great importance in research and industry fields. They allow minimizing the learning aspects and guaranteeing a fixed number of products per day. This paper introduces a new problem that combines the multi-manned concept with the U-shaped lines with time and space constraints under uncertainty. The processing time of the tasks is considered as random variables with known means and variances. Therefore, chance-constraints appear in the cycle time constraints. In addition, each task has an associated area, where the assigned tasks per station are restricted by a total area. The proposed algorithm for solving the problem is a stochastic local search algorithm. The parameter levels of the proposed algorithm are optimized by the Taguchi method to cover the small, medium, and large-sized problems. Well-known benchmark problems have been adapted to cover the new model. The computational results showed the importance of the new problem and the efficiency of the proposed algorithm.