We investigate superconducting pairing of electrons when coupled to an adjacent layer of holes in a GaAs semiconductor heterostructure. When the density of the electrons is much higher than the density of holes, the repulsive electron-electron interaction is reduced by dynamical coupling to the strongly correlated holes. For the effective-mass ratio of electrons to holes in GaAs we find that the effective electron-electron interaction becomes attractive when the layer separation is smaller than a critical value. With equal effective masses this effect does not occur. We estimate the attraction and repulsion parameters for a superconducting state in the electron layer. A typical value of the superconducting transition temperature for experimentally accessible carrier densities and layer separations is Tc=100 mK.