In recent years, dielectric elastomer actuators (DEA) have been investigated as artificial muscle for soft robots, thanks to their light weight, high energy density, and silent operation. Moreover, the low stiffness of the dielectric elastomer (DE) material allows DEA to exhibit large actuation strain. On the other hand, the intrinsic softness of DEA limits their blocking and holding force. Therefore, incorporating variable stiffness structures into DEA is necessary to leverage both large actuation strain, and large holding force from such actuators. This work describes the modeling, fabrication, and characterization of a variable-stiffness DEA (VSDEA) based on interlaminar electrostatic chucking. The VSDEA consists of a multitude of stacked multilayer unimorph DEA units, where each unit consists of a passive layer and one or more active DE layers whose expansion under applied voltage induces bending of the DEA unit. Adhesion between the DEA units is mediated by electrostatic attraction caused by opposite charges accumulating on the interfacial surfaces between each unit. The bending stiffness of the VSDEA is controlled by increasing or decreasing the charge on the interfacial surfaces; large deformation can be achieved when the unit interfaces are allowed to freely slip, and a large increase in stiffness is realized when electrostatic chucking is applied.