This study will look at the safety, tolerability and effectiveness of cidofovir in kidney transplant patients who have been diagnosed with BK virus nephropathy (BKVN), a viral condition that can cause patients to reject transplanted kidneys. Up to 48 adult (age 18 years and older) kidney or pancreas transplant recipients with newly diagnosed BKVN will receive 1 of 3 cidofovir dose levels or placebo (non medicated substance) to identify the maximum tolerated dose. Dosing will be administered intravenously (by a tube running into a blood vessel). In addition to the screening visit, volunteers will actively participate for approximately 8-10 weeks with a single follow up phone call at 4 months. Blood samples, urine samples, eye exams and physical exams are included in study procedures.