Electrorheology (ER) denotes the control of a material's flow properties (rheology) through an electric field. We have fabricated electrorheological suspensions of coated nanoparticles that show electrically controllable liquid-solid transitions. The solid state can reach a yield strength of 130 kPa, breaking the theoretical upper bound on conventional ER static yield stress that is derived on the general assumption that the dielectric and conductive responses of the component materials are linear. In this giant electrorheological (GER) effect, the static yield stress displays near-linear dependence on the electric field, in contrast to the quadratic variation usually observed. Our GER suspensions show low current density over a wide temperature range of 10-120 degrees C, with a reversible response time of <10 ms. Finite-element simulations, based on the model of saturation surface polarization in the contact regions of neighbouring particles, yield predictions in excellent agreement with experiment.