Using high-resolution thermal expansion and magnetization measurements, we provide experimental evidence for a kinetic glass transition in the vortex matter of YBa2Cu3O7-δ with some disorder. This transition, which represents the true superconducting transition in a magnetic field, exhibits many of the features of the usual glass transition found in supercooled structural liquids such as window glass. We demonstrate, using both kinetic and thermodynamic criteria, that this vortex matter is the most fragile system known to date, which we argue makes it possible to investigate the behavior very close to the Kauzmann temperature. Vortex matter, we suggest, may be a model system to study glassy behavior in general, which is expected to lead to a better understanding of the strong-fragile behavior in structural glasses.