High-quality thin polycrystalline films of the heavy-fermion compound CeCu 6 were prepared by sputter deposition. The thicker of these films ͑with thickness up to around 200 nm͒ reproduce the properties of the bulk compound CeCu 6 . As the thickness of the films is decreased, our measurements display strong deviations from the bulk properties, namely, a suppression of the heavy-fermion state. We show that possible ''external'' effects, such as disorder, oxidation and morphology can be excluded and that this size effect is therefore an intrinsic property of CeCu 6 . In addition, we investigate possible scenarios explaining the size effect, and find that the proximity of CeCu 6 to a quantum phase transition can account for this striking result.