A Orthogonal Time Frequency Space (OTFS) system has demonstrated its potential advantages in high-mobility communication scenarios. A low complexity detection algorithm is always a critical challenge for the OTFS receiver. In this paper, we propose a novel detection chain based low-complexity successive interference cancellation (SIC) symbol detection algorithm for OTFS system. Specifically, we first set a protection interval in OTFS data frames, which can provide some inter-symbol interference (ISI)-free areas in received signals. Based on these ISI-free areas, we can construct the detection chain to determine the detection order of the SIC algorithm based on the association relationship of received signals. Furthermore, in order to mitigate the error propagation of the SIC algorithm, we propose a detection direction selection scheme, which can provide the direction selection gain and significantly improve the performance. Moreover, we analyze the complexity of the proposed SIC algorithm. Compared with many existing detection algorithms, the proposed SIC algorithm can significantly reduce the detection complexity. Simulation results show that in the channel scenario with the line of sight (LOS) path, the proposed algorithm outperforms that of message passing (MP) and maximal ratio combining (MRC) algorithms at high SNRs. Furthermore, in the channel scenario without the LOS path, the proposed algorithm is close to MP and MRC algorithms.