We demonstrate the excitation of dark plasmon modes with linearly polarized light at normal incidence in self-assembled layers of gold nanoparticles. Because of field retardation, the incident light field induces plasmonic dipoles that are parallel within each layer but antiparallel between the layers, resulting in a vanishing net dipole moment. Using microabsorbance spectroscopy we measured a pronounced absorbance peak and reflectance dip at 1.5 eV for bi- and trilayers of gold nanoparticles with a diameter of 46 nm and 2 nm interparticle gap size. The excitations were identified as dark interlayer plasmons by finite-difference time-domain simulations. The dark plasmon modes are predicted to evolve into standing waves when further increasing the layer number, which leads to 90% transmittance of the incident light through the nanoparticle film. Our approach is easy to implement and paves the way for large-area coatings with tunable plasmon resonance.