Inclusion Criteria:
1. Willing and able to give informed consent.
2. Willing and able to comply with the prescribed treatment protocol and evaluations for the duration of the trial.
3. Adult men or women ≥18 and \<80 years of age.
4. Uncontrolled gout, defined as meeting the following criteria:
* Hyperuricemia during the screening period defined as sUA ≥6 mg/dL, and;
* Failure to maintain normalization of sUA with xanthine oxidase inhibitors at the maximum medically appropriate dose, or with a contraindication to xanthine oxidase inhibitor therapy based on medical record review or subject interview, and;
* Symptoms of gout including at least 1 of the following:
* Presence of at least one tophus
* Recurrent flares defined as 2 or more flares in the past 12 months prior to screening
* Presence of chronic gouty arthritis as evidenced by either clinical signs consistent with chronic synovitis on clinical examination or the presence of typical gouty erosion(s) on hand and/or foot X-rays
5. Willing to discontinue any oral urate lowering therapy for at least 7 days prior to MTX dosing at Week -4 and remain off while receiving pegloticase treatments.
6. Women of childbearing potential (including those with an onset of menopause \<2 years prior to screening, non-therapy-induced amenorrhea for \<12 months prior to screening, or not surgically sterile \[absence of ovaries and/or uterus\]) must have negative serum/urine pregnancy tests during Screening and Week -4; subjects must agree to use 2 reliable forms of contraception during the trial, one of which is recommended to be hormonal, such as an oral contraceptive. Hormonal contraception must be started ≥1 full cycle prior to Week -4 (start of MTX) and continue for 4 weeks/30 days after the last dose of pegloticase, or at least one ovulatory cycle after the last dose of MTX (whichever is the longest duration after the last dose of pegloticase or MTX). Highly effective contraceptive methods (with a failure rate \<1% per year), when used consistently and correctly, include implants, injectables, combined oral contraceptives, some intrauterine devices, sexual abstinence, or vasectomized partner.
7. Men who are not vasectomized must agree to use appropriate contraception so as to not impregnate a female partner of reproductive potential during the trial, beginning with the initiation of MTX at Week -4 and continuing and for at least 3 months after the last dose of MTX.
8. Able to tolerate MTX 15 mg orally for 4 weeks (Week -4 through Day 1) prior to enrollment.
Exclusion Criteria:
1. Weight \>160 kg (352 pounds) at Screening.
2. Any serious acute bacterial infection, unless treated and completely resolved with antibiotics at least 2 weeks prior to the Day 1 Visit.
3. Severe chronic or recurrent bacterial infections, such as recurrent pneumonia or chronic bronchiectasis.
4. Current or chronic treatment with systemic immunosuppressive agents such as MTX, azathioprine, or mycophenolate mofetil; prednisone ≥10 mg/day or equivalent dose of other corticosteroid on a chronic basis (3 months or longer) would also meet exclusion criteria.
5. History of any transplant surgery requiring maintenance immunosuppressive therapy.
6. Known history of hepatitis B virus surface antigen positivity or hepatitis B DNA positivity.
7. Known history of hepatitis C virus RNA positivity, unless treated and viral load is negative.
8. Known history of Human Immunodeficiency Virus (HIV) positivity.
9. Glucose-6-phosphate dehydrogenase deficiency (tested at the Screening Visit centrally or locally).
10. Chronic renal impairment defined as estimated glomerular filtration rate (eGFR) \<40 mL/min/1.73 m\^2 or currently on dialysis.
11. Non-compensated congestive heart failure or hospitalization for congestive heart failure within 3 months of the Screening Visit, uncontrolled arrhythmia, treatment for acute coronary syndrome (myocardial infarction or unstable angina), or uncontrolled blood pressure (\>160/100 mmHg) prior to enrollment at Day 1.
12. Pregnant, planning to become pregnant, breastfeeding, planning to impregnate female partner, or not on an effective form of birth control, as determined by the Investigator.
13. Prior treatment with pegloticase, another recombinant uricase (rasburicase), or concomitant therapy with a polyethylene glycol-conjugated drug.
14. Known allergy to pegylated products or history of anaphylactic reaction to a recombinant protein or porcine product.
15. Contraindication to MTX treatment or MTX treatment considered inappropriate.
16. Known intolerance to MTX.
17. Receipt of an investigational drug within 4 weeks or 5 half-lives, whichever is longer, prior to MTX administration at Week -4 or plans to take an investigational drug during the trial.
18. Liver transaminase levels (AST or ALT) \> 1.25 X upper limit of normal (ULN) or albumin \< the lower limit of normal (LLN) at the Screening Visit.
19. Chronic liver disease.
20. White blood cell count \<4000/µl, hematocrit \<32 percent, or platelet count \<75,000/µl.
21. Currently receiving systemic or radiologic treatment for ongoing cancer, excluding non-melanoma skin cancer.
22. History of malignancy within 5 years other than non-melanoma skin cancer or in situ carcinoma of cervix.
23. Diagnosis of osteomyelitis.
24. Known history of hypoxanthine-guanine phosphoribosyl-transferase deficiency, such as Lesch-Nyhan and Kelley-Seegmiller syndrome.
25. Unsuitable candidate for the trial, based on the opinion of the Investigator (e.g., cognitive impairment), such that participation might create undue risk to the subject or interfere with the subject's ability to comply with the protocol requirements or complete the trial.
26. Alcohol use in excess of 3 alcoholic beverages per week.
27. A known intolerance to all protocol standard gout flare prophylaxis regimens (i.e., subject must be able to tolerate at least one: colchicine and/or non-steroidal anti-inflammatory drugs and/or low dose prednisone ≤10 mg/day).
28. Current pulmonary fibrosis, bronchiectasis or interstitial pneumonitis. If deemed necessary by the Investigator, a chest X-ray may be performed during Screening.
