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Retaining persons living with HIV (PLWH) in medical care is paramount to preventing new transmissions of the virus and allowing PLWH to live normal and healthy lifespans. Maintaining regular appointments with an HIV provider and taking medication daily for a lifetime is exceedingly difficult. 51% of PLWH are non-adherent with their medications and eventually drop out of medical care. Current methods of re-linking individuals to care are reactive (after a patient has dropped-out) and hence not very effective. We describe our system to predict who is most at risk to drop-out-of-care for use by the University of Chicago HIV clinic and the Chicago Department of Public Health. Models were selected based on their predictive performance under resource constraints, stability over time, as well as fairness. Our system is applicable as a point-of-care system in a clinical setting as well as a batch prediction system to support regular interventions at the city level. Our model performs 3x better than the baseline for the clinical model and 2.3x better than baseline for the city-wide model. The code has been released on github and we hope this methodology, particularly our focus on fairness, will be adopted by other clinics and public health agencies in order to curb the HIV epidemic.