Dynamical heterogeneity and the decoupling of diffusion and relaxation in a supercooled liquid is investigated via a time-dependent, four-point density correlation function. We show that the main contribution to the corresponding generalized susceptibility chi(4)(t) in a molecular dynamics simulation of a Lennard-Jones liquid arises from spatial correlations between temporarily localized ("caged") particles. By comparing chi(4)(t) with a generalized susceptibility chi(M)(t) related to a correlation function for the squared particle displacements, we demonstrate a connection between dynamical heterogeneity and the decoupling of relaxation and diffusion.