The polarization of light plays a central role in its interaction with matter, in situations ranging from familiar (for example, reflection and transmission at an interface) to sophisticated (for example, nonlinear optics). Polarization control is therefore pivotal for many optical systems, and achieved using bulk devices such as wave-plates and beam-splitters. The move towards optical system miniaturization therefore motivates the development of micro-and nanostructures for polarization control. For such control to be complete, one must distinguish not only between linear polarizations, but also between left-and right-circular polarizations. Some previous works used surface plasmons to this end, but these are inherently lossy. Other works used complex-layered structures. Here we demonstrate a planar dielectric chirality-distinguishing beam-splitter. The beam-splitter consists of amorphous silicon nanofins on a glass substrate and deflects left-and right-circularly polarized beams into different directions. Contrary to intuitive expectations, we utilize an achiral architecture to realize a chiral beam-splitting functionality.