With Universal Pre-K (UPK) receiving renewed attention at national and state levels, one question that policy developers must address is how many families will participate if high quality preschool education is offered to all 3- and 4-year-olds at no cost to their families. The few current statewide UPK programs—including those that start at age 3 in the District of Colombia and Vermont—are difficult to generalize to the rest of our highly diverse nation. To obtain more insight, NIEER asked a nationally representative sample of parents of 3- to 5-year-olds how they would respond to UPK. The survey was conducted from late May to early June, 2021 and included 794 parents whose children could be eligible for UPK next fall. Despite lingering concerns about the pandemic, 81 percent said they would be very (60%) or somewhat (21%) likely to enroll their children if offered free, high-quality pre-K in the fall. Few parents said they were not at all (13%) or not very (7%) likely to enroll a child in UPK. An 81 percent enrollment rate would be a substantial increase over recent rates of preschool participation. (author abstract)