This paper presents a new Abductive Logic Programming (ALP) approach for assisting clinicians in the selection of anti-retroviral drugs for patients infected with Human Immunodeficiency Virus (HIV). The approach is comparable to laboratory genotypic resistance testing in that it aims to determine which viral mutations a patient is carrying and predict which drugs they are most likely resistant to. But, instead of genetically analysing samples of the virus taken from patients -- which is not always practicable -- our approach infers likely mutations using the patient's full clinical history and a model of drug resistance maintained by a leading HIV research agency. Unlike previous applications of abduction, our approach does not attempt to find the "best" explanations, as we can never be absolutely sure which mutations a patient is carrying. Rather, the intrinsic uncertainty of this domain means that multiple ternative explanations are inevitable and we must seek ways to extract useful information from them. The computational and pragmatic issues raised by this approach have led us to develop a new ALP methodology for handling numerous explanations and for drawing predictions with associated levels of confidence. We present our in-Silico Sequencing System (iS3) for reasoning about HIV drug resistance as a concrete example of this approach.