Muon spin relaxation is a remarkably powerful tool for discovering magnetic order in quasi-one-dimensional magnetic chain compounds, particularly when the weak interchain coupling and quantum fluctuations suppress both the Néel temperature and the ordered magnetic moment. Here we propose to study a newly synthesized S=1/2 copper chain compound in which bulk measurements have failed to find magnetic order down to 0.1K. Having compared the results of this study to theoretical models we anticipate that this material should order at close to 0.1K, but with a strongly reduced magnetic moment which would almost certainly have been insufficient to be observed in the previous study, but should be clearly apparent to muons. We also intend to study the spin fluctuations as a function of longitudinal field above the ordering transition, or at base temperature if no ordering is apparent.