This study will enroll HIV-infected adults on combination antiretroviral therapy (cART) who need a kidney transplant. At the time of their kidney transplant, study participants will be randomly assigned to receive either MVC or placebo as an addition to their cART regimen. (MVC or placebo will be provided by the study. However, the HIV medicines in their cART regimens will not be provided by the study.) Participants will receive MVC or placebo throughout their participation in the study, which will be 1 to 3 years depending on when they enroll in the study.