In version 3.0 of this study, participants who test positive for CMV viremia or who are currently in Step 2 will be automatically enrolled into Step 4 and will be randomly assigned to one of two groups: 1) 900 mg valganciclovir twice daily for 3 weeks, followed by 900 mg valganciclovir daily, or 2) placebo. Participants will enter Step 3 if and when they develop CMV end-organ disease, at which point all participants will be offered 900 mg valganciclovir twice daily for 3 weeks, then 900 valganciclovir daily thereafter.