We develop a theory of the adsorption of many polyampholyte chains on a charged surface. The adsorption is due to the polarization of polyampholyte chains in the external electric field created by the charged surface. The equilibrium polymer density profile is determined by balancing the long-range polarization-induced attraction of polyampholytes to the charged surface and the three-body repulsion between monomers in a theta-solvent for the polymer backbone (or the two-body repulsion in a good solvent). We demonstrate that the long-range nature of polyampholyte adsorption can lead to an adsorbed layer much thicker than the size of individual chains. Adsorbed polyampholytes that do not touch the surface form a multibrush of stretched chains. The chains that touch the surface form a self-similar stretched pseudobrush. Polyampholyte chains carrying the net charge of the same sign as that of the surface can also adsorb. In this case, the adsorption stops at that distance from the surface where the electrostatic repulsion between polyampholytes and a similarly charged surface becomes stronger than the polarization-induced attraction. The thickness of the adsorbed layer and the surface coverage decrease with increasing net charge on polyampholytes. The effect sf added salt on polyampholyte adsorption is also discussed.