The strong optical chirality arising from certain synthetic metamaterials has important and widespread applications in polarization optics, stereochemistry and spintronics. However, these intrinsically chiral metamaterials are restricted to a complicated three-dimensional (3D) geometry, which leads to significant fabrication challenges, particularly at visible wavelengths. Their planar two-dimensional (2D) counterparts are limited by symmetry considerations to operation at oblique angles (extrinsic chirality) and possess significantly weaker chiro-optical responses close to normal incidence. Here, we address the challenge of realizing strong intrinsic chirality from thin, planar dielectric nanostructures. Most notably, we experimentally achieve near-unity circular dichroism with ~90% of the light with the chosen helicity being transmitted at a wavelength of 540 nm. This is the highest value demonstrated to date for any geometry in the visible spectrum. We interpret this result within the charge-current multipole expansion framework and show that the excitation of higher-order multipoles is responsible for the giant circular dichroism. These experimental results enable the realization of high-performance miniaturized chiro-optical components in a scalable manner at optical frequencies.