Inclusion Criteria:

1. Male or a post-menopausal or surgically sterile female.
2. 18 - 80 years of age.
3. Has been taking allopurinol as the sole urate lowering therapy for hyperuricemia for at least 6 weeks at a dose between 200 mg and 600 mg per day without an adequate response.
4. Has a sUA level ≥ 6 mg/dL at screening.
5. Meets criteria for the diagnosis of gout as per the American Rheumatism Association (ARA) Criteria for the Classification of Acute Arthritis of Primary Gout.
6. Willing and able to give informed consent and adhere to visit/protocol schedules (informed consent must be given before the first study procedure is performed).
7. Subjects entering the optional Extension Period must have completed 28 days of dosing in the Double-Blind Treatment Period and the Day 42 Visit in the Follow-up Period within 4 months and must not have experienced any serious adverse events considered possibly related to study drug.
8. Subjects entering the optional Open-Label Extension Period must continue to be compliant with the protocol through Week 44 of the Double-Blind Extension Period and must not have experienced any serious adverse events considered possibly related to study drug.

Exclusion Criteria:

1. Consumes more than 14 drinks of alcohol per week (e.g., 1 drink = 5 oz [150 ml] of wine, 12 oz [360 ml] of beer, or 1.5 oz [45 ml] of hard liquor).
2. History or suspicion of drug abuse.
3. History of documented or suspected kidney stones.
4. Has rheumatoid arthritis or other autoimmune disease requiring treatment.
5. Documented or suspicion of HIV infection.
6. Positive serology to HCV antibodies (Abs), and/or hepatitis B surface antigen (HBsAg).
7. History of malignancy within 5 years prior to the first dose of study medication, other than non-melanomatous skin cancer or cervical dysplasia.
8. History of cardiac abnormalities, including abnormal and clinically relevant ECG changes
9. Any condition predisposing to QT prolongation including pathological Q-wave (defined as Q-wave >40 msec or depth > 0.4-0.5 mV).
10. Any use of concomitant medications that prolong the QT/QTc interval within the 14 days prior to Baseline (Day 1).
11. QT interval corrected for heart rate according to Fridericia (QTcF) > 450 msec at Screening or pre-dose at Baseline (Day 1).
12. Uncontrolled hypertension (above 150/95).
13. Inadequate renal function [serum creatinine >1.5 mg/dL or creatinine clearance < 60 mL/min (by Cockroft-Gault formula)].
14. Hemoglobin < 10 g/dL (males) or < 9 g/dL (females).
15. Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) > 2.5 x upper limit of normal (ULN).
16. Gamma glutamyl transferase (GGT) > 3 x ULN.
17. Active peptic ulcer disease requiring treatment.
18. History of xanthinuria, active liver disease, or hepatic dysfunction.
19. Requires therapy with any other urate-lowering medication, other than the study medications.
20. Requires long-term use of salicylates; diuretics; losartan; azathioprine; mercaptopurine; theophylline; intravenous colchicine; cyclosporine; cyclophosphamide; pyrazinamide; sulfamethoxazole; or trimethoprim.
21. Taking medications known as enzyme inducers (see section 3.7 for listing).
22. Reports receiving a strong or moderate inhibitor of CYP3A4 or a P-gp inhibitor within 1 month prior to study drug dosing, due to potential interactions with colchicine.
23. Acute gout flare (exclusive of chronic synovitis/ arthritis) during the Screening-Period that has not resolved one week prior to the Baseline Visit (Day 0).
24. Pregnant or breast feeding.
25. Has received an investigational medication within 4 weeks prior to the screening visit for this study.
26. Previously participated in a clinical study involving RDEA806 or RDEA594.
27. Known hypersensitivity or allergy to RDEA594, allopurinol or colchicine or any components in their formulations.
28. Body mass index (BMI) >48 kg/m2.
29. Taking greater than 1000 mg/day of Vitamin C.
30. Any other medical or psychological condition, which in the opinion of the Investigator and/or Medical Monitor, might create undue risk to the subject or interfere with the subject's ability to comply with the protocol requirements, or to complete the study.
31. Inadequate renal function after completing the Double-Blind Treatment period prior to entering Double-Blind Extension Period.
32. Requiring treatment with prohibited medications noted in exclusion criteria numbers 20-23 after completing the Double-Blind Treatment Period prior to entering the Extension Period.
33. Clinically relevant medical event as determined by the investigator in consultation with medical monitor prior to entering the Extension Period.