Structural relaxation in an undercooled liquid confined between two parallel structureless plates is investigated by molecular dynamics simulations. It is found that the system exhibits a kinetic glass transition, detected as a crossover from hydrodynamic relaxation to a relaxation dominated by hopping processes. The kinetic transition occurs at significantly smaller densities than that of the bulk glass transition. In particular, the dependence of this density shift on the plate distance L is studied for systems involving 3 to 16 microscopic layers in between the plates. As a result, the density shift scabs approximately proportionally to exp( -L/l(0)) where l(0) is a microscopic length scale. Furthermore, the kinetic glass transition is a collective effect that occurs simultaneously in each layer.