CC-11050 in Human Immunodeficiency Virus-1-Infected Adults With Suppressed Plasma Viremia on Antiretroviral Therapy (APHRODITE)

* INCLUSION CRITERIA: 1. Adults (greater than or equal to 18 years) 2. Body mass index (BMI) less than or equal to 35 kg/m2 3. On ART for a minimum of 1 year and on a stable regimen (according to DHHS guidelines) for at least 3 months prior to screening 4. Plasma HIV-1 RNA level \<50 copies/mL at screening (patients with 50-499 \<500 copies/mL at screening may be asked to return for rescreening in four (4) weeks or later 5. Men and women must be willing to take appropriate precautions to prevent pregnancy as described below 6. Willingness to undergo genetic testing 7. Willingness to allow storage of specimens for future analysis 8. Negative serum or urine pregnancy test (for women of childbearing potential) 9. Under the care of a primary care physician outside of the NIH Contraception: The effects of CC-11050 on the developing human fetus are unknown. For this reason, subjects must agree to not become pregnant. Females of childbearing potential must have a pregnancy test before initiating the study agent and at each study visit. Because of the risk involved, male and female study participants who engage in sexual activities that can result in pregnancy must agree to use of a male or female condom at every potentially reproductive sexual encounter, AS WELL AS one of the other methods listed below, beginning at the baseline visit and continuing until 3 months after discontinuation of the study agent. Acceptable methods are as follows: * Hormonal contraception \[e.g. consistent use of oral contraceptive pill daily or other hormonal method such as contraceptive implant or injection\] (must be started 1 month prior to receiving the first dose of study agent) * Diaphragm or cervical cap * Intrauterine device (IUD) * Male partner with a vasectomy During the study, if a participant becomes pregnant or suspects they are pregnant, they should inform the study staff and their primary care physician immediately. The study medication will be stopped immediately and if on CC-11050 they will be referred to a high risk pregnancy specialist and followed by the study team for the remainder of the pregnancy or the rest of the study, whichever occurs later. EXCLUSION CRITERIA: 1. Body mass index (BMI) less than or equal to 18.5 kg/m2 2. Protease inhibitor-based ART regimen 3. ART regimen which includes Cobicistat 4. Absence of alternate available ART options in case of virologic failure 5. Serum ALT or AST value Grade \>2 or total bilirubin greater than the ULN unless it is indirect due to Gilbert s disease 6. History of chronic hepatitis B (+HbsAg or +HBV DNA in plasma) and/or C - treated chronic hepatitis C with SVR \> 2 years will be accepted. 7. Cirrhosis of the liver, or any known active or chronic liver disease 8. Recent history (\<30 days) of infection requiring inpatient hospitalization or systemic therapy 9. Depression. Patients who report depression or, are suspected or known to have depression and are on stable anti-depressants will undergo Psychiatry evaluation and clinical assessments to determine eligibility. These assesments will be done by a psychiatrist and may include: Beck Depression Inventory (BDI), Spielberger State-Trait Anxiety Inventory (STAI), Montreal Cognitive Assessment(MoCA). The BDI, STAI, and MoCA will be administered to patients being considered for study enrollment. The BDI and STAI may be repeated at least once during follow-up visits in those deemed eligible to participate. 10. Current breastfeeding 11. Current or anticipated treatment with immunomodulating agents (such as systemic corticosteroids, interleukins, interferons) or any agent with known anti-HIV activity (other than antiretrovirals approved for use in the treatment of HIV) 12. Any experimental medications within 4 weeks prior to screening or anticipated use of such medications during the trial. 13. Current (4 weeks prior to the first dose of study drug,) or anticipated use of antimetabolites; alkylating agents; or drugs other than ART, herbal preparations (including St. John s wort), and foods (including grapefruit) known to affect activity of the CYP3A4 enzyme pathway 14. Use of thalidomide, lenalidomide, pomalidomide, systemic corticosteroids within 4 weeks of screening 15. Any prior history of PDE4 inhibitor use 16. History of pancreatitis, elevated lipase (less than or equal to 1.5 above the upper limit of normal) or triglyceride level \>500 mg/dL. 17. History of clinically significant metabolic, endocrine, hepatic, renal, hematologic, pulmonary, gastrointestinal, autoimmune or cardiovascular disorders 18. Uncontrolled hypertension (persistent measurements over 140/90) 19. Bradycardia, defined as a sinus rhythm \<50 beats/min (bpm) 20. History or presence of a clinically significant abnormal ECG 21. History of malignancy except cured basal or squamous cell carcinoma of the skin or cutaneous Kaposi s sarcoma not requiring systemic therapy during the trial 22. Receipt of radiation or cytotoxic chemotherapeutic agents, unless fully recovered from disease by the time of the first dose of study drug as determined by the opinion of the Investigator, or anticipated use of such agents during the study period 23. Any condition or significant problems that, based on the judgment of the investigator, would increase risk to the subject or would interfere with the subject s ability to comply with protocol requirements. Co-enrollment Guidelines: Co-enrollment in other trials is restricted, other than enrollment on observational studies or those evaluating the use of a licensed medication. Study staff should be notified of co-enrollment as it may require the approval of the study investigators.