This study will last up to 4 years. Participants will undergo kidney transplantation on Day 0 and will receive intravenous doses of alemtuzumab, acetaminophen, and diphenhydramine on Days 0, 1, and 2, as well as methylprednisolone on Day 0. After transplant, patients will receive up to 10 days of valganciclovir or acyclovir. Participants will take tacrolimus daily by mouth for at least 60 days after transplant and sirolimus daily by mouth for at least 12 months after transplant. As part of opportunistic infection (OI) prophylaxis, participants will also take sulfamethoxazole-trimethoprim by mouth 3 times a week, valganciclovir or acyclovir for up to 10 days post-transplant, and clotrimazole or nystatin by mouth for at least 3 months post-transplant.