The possibility of tailoring physical properties by changing the number of layers in van der Waals crystals is one of the driving forces behind the emergence of two-dimensional materials. One example is bulk MoS2, which changes from an indirect gap semiconductor to a direct bandgap semiconductor in the monolayer form. Here, we show a much bigger tuning range with a complete switching from a metal to a semiconductor in atomically thin PtSe2 as its thickness is reduced. Crystals with a thickness of ~13 nm show metallic behavior with a contact resistance as low as 70 Ω·µm. As they are thinned down to 2.5 nm and below, we observe semiconducting behavior. In such thin crystals, we demonstrate ambipolar transport with a bandgap smaller than 2.2 eV and an on/off ratio of ~105. Our results demonstrate that PtSe2 possesses an unusual behavior among 2D materials, enabling novel applications in nano and optoelectronics.