Cognitive impairment, including disabling cognitive, behavioral, and social dysfunction, continues to be a major problem faced by HIV-infected people taking antiretroviral therapy (ART). Research is needed to develop treatment that can be given alongside ART to prevent or lessen cognitive impairment caused by ART. Minocycline, an antibiotic commonly used for the treatment of acne and rheumatoid arthritis, has demonstrated anti-inflammatory and neuroprotective properties in previous studies. This study will evaluate the effectiveness of 24-week therapy with minocycline in lessening the cognitive impairment of HIV infected adults taking ART.