Inclusion Criteria:

1. Age ≥ 18 to < 70 years
2. Have read and signed the Informed Consent Form
3. Documented diagnosis of gout
4. Documented moderate renal insufficiency
5. Calculated creatinine clearance of ≥ 30 and < 60 mL/min
6. Willing and able to take allopurinol 200 mg every day for the duration of the Treatment
7. Female participants must be sexually abstinent for 4 weeks prior to Day 1 and continue abstinence for 4 weeks after completion of study drug, surgically sterile, postmenopausal,use oral contraceptives for three months prior to study drug dosing through 4 weeks after completion of study drug, an intrauterine device for 8 weeks prior to study drug dosing through 4 weeks after completion of study drug,double barrier contraception method for 4 weeks prior to study drug dosing through 4 weeks after completion of study drug administration
8. Male participants must be sexually abstinent for 4 weeks prior to Day 1 and continue abstinence through 90 days after completion of study drug, be > 1 year postvasectomy, agree to use a condom with spermicide from the start of study drug dosing through 90 days after completion of study drug.
9. Willing and able to provide authorization for the use and disclosure of personal health information in accordance with Health Insurance Portability and Accountability Act (HIPAA)

Exclusion Criteria:

1. Unable to tolerate allopurinol 200 mg every day
2. Prior randomization in a clinical study with BCX4208
3. Unstable cardiac disease such as: unstable angina, symptomatic arrhythmia, signs or symptoms compatible with NYHA Class III or Class IV functional status for congestive heart failure or angina, history of long QT syndrome, or QTc interval < 350 msec or > 475 msec
4. Poorly controlled hypertension
5. History of severe renal insufficiency
6. Alanine aminotransferase or aspartate aminotransferase values > 2.0 x upper limit of normal
7. CD4+ cell counts by flow cytometry < 500 cells/mm3
8. Hemoglobin < 10 g/dL or > 18 g/dL (males) or < 10 g/dL or > 17 g/dL (females)
9. White blood cell count < 3.7 x 109/L or > 11 x 109/L
10. Female subjects who are pregnant, breastfeeding, or planning a pregnancy within the next 4 months
11. Positive serology for hepatitis B surface antigen or hepatitis C antibody or HIV type 1
12. Immunocompromised due to illness or organ transplant
13. Use of systemic immunosuppressive medications or disease-modifying antirheumatic drugs
14. Use of azathioprine or 6-mercatopurine within 14 days of first dose of allopurinol
15. Use of hydrochlorothiazide in doses > 50 mg per day
16. Planned use of herbal or dietary supplements
17. Recipient of any live or attenuated vaccine within 6 weeks of Screening
18. Planned use of uric acid-lowering drugs other than allopurinol
19. Use of systemic corticosteroids within 4 weeks prior to Day 1
20. Use of any investigational drug within 30 days prior to signing the ICF
21. History of clinically significant and relevant drug allergies
22. History of chronic or recurrent infections
23. History of any type of cancer not successfully treated or in full remission for 12 months prior to Screening
24. History of alcohol or drug abuse within the year prior to the signing of the ICF, or current evidence of substance dependence or abuse
25. Use of other prohibited medications within the timeframes specified in the protocol
26. Other medical conditions which, in the opinion of the Principal Investigator, would jeopardize the safety of the study subject