In this paper, we present a successive-cancellation-soft-output (SCSO) detector for an uplink multiuser multiple-input-multiple-output (MU-MIMO) system with one-bit analog-to-digital converters (ADCs). The proposed detector produces soft outputs (e.g., log-likelihood ratios (LLRs)) from one-bit quantized observations in a successive way: each user k's message is sequentially decoded from a channel decoder $k$ for $k=1,...,K$ in that order, and the previously decoded messages are exploited to improve the reliabilities of LLRs. Furthermore, we develop an efficient greedy algorithm to optimize a decoding order. Via simulation results, we demonstrate that the proposed ordered SCSO detector outperforms the other detectors for the coded MU-MIMO systems with one-bit ADCs.