We present the first high-resolution study of the aqueous structure developed in the electrical double layer region of a colloidal clay system. Our samples were highly oriented vermiculite gels containing isotopically labelled propylammonium counterions : C3H7NH3+ and C3D7NH3+ The gels were prepared with a clay layer spacing of 43.6 Angstrom. Time-of-flight neutron diffraction was used to measure the scattering intensity normal to the clay surfaces, from which the neutron scattering density was refined by an inverse Monte Carlo method. Diffraction data from two isotopically distinct samples were fitted simultaneously, thereby allowing us to locate the labelled propyl groups unambiguously. Our results show that the counterions in our vermiculite gels are separated from the clay surfaces by two layers of partially ordered water molecules. In fact, the counterion density reaches a maximum at the center of the interlayer region. The measured structure is therefore at odds with traditional primitive models of the electrical double layer. Such models place the maximum of the counterion density adjacent to the vermiculite clay surfaces, in the so-called Stern layer.