The purposes of this study are: to make sure that there are no serious side effects of an experimental inactivated influenza A/H5N1 vaccine in children; and to see how the body's immune system reacts to the vaccine. To look at the side effects, researchers will follow children closely after vaccination. To look at immune system responses, researchers will test the children's blood before and a number of times after vaccination. Participants will include up to 130 healthy children ages 2-9 years. Participants will be assigned to receive 2, up to 3 doses of vaccine, or placebo (inactive substance). Subjects will receive at least 2 doses of vaccine approximately 28 days apart. If data shows an enhanced immune response from a third vaccination, children will be offered a third dose of the vaccine. Participants will be involved in study related procedures for up to 13 months, including up to 6 study visits, plus a number of telephone calls.