 The total study duration will be 36 weeks. Prior to enrolling in the study, participants will have a chest X-ray. Participants will be randomly assigned to receive LDMTX or placebo for 24 weeks. Participants will continue taking their antiretroviral ARV medications as usual; ARVs will not be provided by the study. At study entry, participants will undergo a medical and medication history, physical examination, blood collection, and adherence assessments. From study entry through Week 1, participants will receive either 5 mg of MTX or placebo once a week. For participants who are clinically stable at the Week 1 study visit, the dose of MTX or placebo will be increased to 10 mg once a week through Week 12. For participants who are clinically stable at the Week 12 study visit, the dose of MTX or placebo will be increased to 15 mg once a week through Week 24. Participants who do not meet the criteria for dose escalation will be re-evaluated at the following study visit. In addition to LDMTX or placebo, all participants will also receive 1 mg of folic acid once a day from study entry throughout Week 24. After taking the final dose of LDMTX or placebo, all participants will continue taking folic acid for an additional 4 weeks. 