This study will test the safety and how well the body's immune system responds to a live, but weakened varicella (chickenpox) vaccine, known as Varivax, given with and without ProQuad, another measles, mumps, rubella, and varicella virus vaccine (MMR-II). One hundred five healthy children will be enrolled in the study when they are 12 months old. All subjects will be vaccinated at 12 months of age and some subjects will receive a second vaccination at 18 months of age. All subjects will participate for 1 year. This study is a single-site, two-year trial with post-licensure vaccines.