Induced chirality in colloidal semiconductor nanoparticles has raised significant attention in the past few years as an extremely sensitive spectroscopic tool and due to the promising applications of chiral quantum dots in sensing, quantum optics, and spintronics. Yet, the origin of the induced chiroptical effects in semiconductor nanoparticles is still not fully understood, partly because almost all the theoretical and experimental studies to date are based on the simple model system of a spherical nanocrystal. Here, the realization of induced chirality in atomically flat 2D colloidal quantum wells is shown. A strong circular dichroism (CD) response as well as an absorptive-like CD line shape is observed in chiral CdSe nanoplatelets (NPLs), significantly differing from that previously observed in spherical dots. Furthermore, this intense CD signal almost completely disappears after coating with a very thin CdS shell. In contrast, CdSe-CdS core-crown NPLs exhibit a spectral response which seems to originate independently from the core and the crown regions of the NPL. This work on the one hand further advances the understanding of the fundamental origin of induced chiroptical effects in semiconductor nanoparticles, and on the other opens a pathway toward applications using chiroptical materials.