Inclusion Criteria:

• Age between 18 - 75 years, inclusive. Males must be able and willing to use adequate contraceptive methods throughout the study and for 3 months after the final dose. Females must be post-menopausal, surgically sterile or willing to use adequate contraception for the duration of the study (screening through the Day 49 visit).
• Renal (Cohorts 3A, 4A, 4B and 4C) or hematopoietic stem cell (Cohort 3A only) transplant patients who meet the following criteria.

Renal transplant patients who:

are at least 28 days post transplant are in stable condition with hemoglobin >10g/100mL (Cohort 3A) or ≥8g/100mL (Cohorts 4A, 4B and 4C)

• have no evidence of graft rejection (i.e., serum creatinine is not increasing (+/- 30%), creatinine clearance is not decreasing)
• have been on a stable immunosuppressant (IS) regimen for at least 14 days prior to dosing. Stable immunosuppression allows for changes that are standard of care for the management of the immunosuppression regimen (e.g., steroid tapering or dose adjustments to maintain trough levels in the therapeutic range). These also include adjustments of dosing due to known side effects of the IS (e.g., GI symptoms with MMF).
• have either urine levels of BKV DNA ≥ 104 copies/mL without viremia or plasma levels of BKV DNA < 104 copies/mL (with or without viruria). -Plasma levels of BKV DNA between 104 - 105 copies/mL will be considered on a case by case basis in consultation with the medical monitor (Cohorts 4A, 4B and 4C).

Stem cell transplant patients (Cohort 3A only) who:

are a minimum of 3 days post documentation of successful engraftment as evidenced by an absolute neutrophil count > 500 cells/mm3 have urine levels of BKV ≥ 104 copies/mL Glomerular filtration rate > 30 mL/min. Able to swallow tablets. Willing and able to understand and provide written informed consent. Willing and able to participate in all required study activities for the duration of the study (including ingestion of oral medication).

Exclusion Criteria:

• Currently nursing or pregnant females.
• Current use of illicit drugs; current abuse of alcohol.
• Subjects with hypersensitivity to cidofovir or CMX001.
• Patients who received aminoglycosides (IV) or NSAIDS (except as given for cardioprotective treatment) within 7 days prior to enrollment; patients who received leflunomide, cidofovir or any other medication for treatment of BK virus infection or disease within 14 days prior to enrollment; patients who received any investigational drug (including maribavir) within 30 days prior to enrollment.
• Patients who are HIV positive (results must be obtained within one year prior to dosing); patients with active HCV or HBV infection as evidenced by plasma levels of HCV RNA or HBV DNA, respectively.
• Renal transplant patients with evidence of biopsy proven acute rejection in the 3 weeks prior to enrollment. This exclusion criteria applies only to those patients for whom a biopsy was performed within the three weeks prior to enrollment.

• Stem cell transplant patients (Cohort 3A only) who:

  1. have cystitis ≥ Grade 3 (NCI, CTCAE v3.0)
  2. have Grade 3 or 4 Graft Versus Host Disease (GvHD)
  3. have untreated or uncontrolled Grade 2 GvHD
  4. received ganciclovir or valganciclovir within 14 days prior to enrollment
• Patients with mucositis preventing ingestion of oral medication.
• Patients with hypotony, uveitis, or retinitis or any intraocular pathology that would predispose the patient to any one of these conditions.
• Patients with unstable or poorly controlled diabetes defined as having frequent hypoglycemic and/or hyperglycemic events on a daily basis (brittle diabetes), with fluctuating short acting insulin requirements daily, or requiring unpredictable insulin supplementation to oral hypoglycemic agents on a regular basis.
• Patients with bilirubin > 2.5 x ULN.
• Patients with cardiovascular disease which, in the opinion of the investigator, would interfere with the conduct of the study.
• Patients with any of the following autoimmune diseases; Addison's disease, autoimmune hemolytic anemia, autoimmune hepatitis, bullous pemphigoid, celiac disease, dermatomyositis, active Goodpasture's syndrome, idiopathic thrombocytopenic purpura, active lupus erythematosus, multiple sclerosis, myasthenia gravis, pemphigus vulgaris, polymyositis, primary biliary cirrhosis, vasculitis, Wegener's granulomatosis.
• Patients with active malignancies (with the exception of basal cell carcinoma or the condition under treatment for HSCT patients).
• Patients with concurrent or ongoing ≥ Grade 2 GI symptoms including nausea, vomiting, diarrhea, constipation or gastroenteritis. Patients with active GI disease including inflammatory bowel disease, irritable bowel syndrome (IBS), or celiac sprue.
• Any other condition including abnormal laboratory values that would in the judgment of the investigator put the subject at increased risk for participating in the trial, or interferes with the conduct of the trial.