A major clinical goal of brain-computer interfaces (BCIs) is to allow severely paralyzed patients to communicate their needs and thoughts during their everyday lives. Among others, P300-based BCIs, which resort to EEG measurements, have been successfully operated by people with severe neuromuscular disabilities. Besides reducing the number of stimuli repetitions needed to detect the P300, a current challenge in P300-based BCI research is the simplification of system's setup and maintenance by lowering the number N of recording channels. By using offline data collected in 30 subjects (21 amyotrophic lateral sclerosis patients and 9 controls) through a clinical BCI with N = 5 channels, in the present paper we show that a preprocessing approach based on a Bayesian single-trial ERP estimation technique allows reducing N to 1 without affecting the system's accuracy. The potentially great benefit for the practical usability of BCI devices (including patient acceptance) that would be given by the reduction of the number N of channels encourages further development of the present study, for example, in an online setting.