This paper has presented a quantitative/stochastic research approach to aspects of a psychotherapy with an HIV-positive patient. The Box-Jenkins (ARIMA) method for time-series analysis was applied to the duration of speaker roles for a single male patient in his first three sessions with a male therapist. The results indicate a definitive underlying stochastic structure of order (1, 1, 1). This indicates that the sequence of speaker durations was nonstationary (chaotic), while the rate at which the sequence changed (velocity) showed a clear structure reflecting the influence on the system of the prior state, and of the prior and present shocks. The histograms of the frequency of utterances of varying time lengths revealed a second deep structure through the emergence of an exponential characteristic of a Poisson model. The Poisson rate constants--a measure of interruption and holding tendencies--were stable across interviews. Intervention analysis identified epochs in each interview that significantly altered the progression of the time series. A qualitative investigation of these periods of destabilization suggested that sudden allusions to highly charged topics, including the likelihood of a fatal outcome of the patient's illness, and especially unconscious criticisms of the therapist by the patient, created a large share of these interludes. Finally, there is a discussion of the limitations and implications of these findings, including a comparison with similar analyses for 6 psychotherapy consultation sessions.