In this paper, we introduce a generalization of the distributed sorting problem on chain network. This problem consists of sorting values in processes that are separated from each other by any number of intermediate processes which can relay values but do not have their own values. We solve this problem in a chain network by proposing a silent self-stabilizing distributed algorithm. This algorithm converges fromanyinitialconfigurationtoaterminalconfigurationwherevaluesaresortedinthechaininincreasing order from left to right