We report the crystal growth and structural and electronic properties of superconducting, van der Waals layered PtTe. Easily cleavable crystals with a platelike morphology consistent with the layered structure were grown from a platinum-rich flux. A consistent determination of Tc=0.57 K is made from the onset of diamagnetism, the zero of resistivity, and the midpoint of the heat-capacity jump. The observed behavior is consistent with type-II superconductivity, with upper critical field at T=0 estimated using the Werthamer-Helfand-Hohenberg theory to be 143 and 65 Oe for fields out of and in the plane, respectively. The heat-capacity discontinuity is close to the weak-coupling BCS value. Density-functional theory calculations and analysis of the electronic structure finds that PtTe is a topological semimetal with numerous surface states but suggests that the superconducting state itself may be topologically trivial. Angle-resolved photoemission spectroscopy reveals a normal-state Fermi surface in remarkable agreement with theory and confirms the overall topological nature of the material by experimental identification of the surface bands. Together, these findings identify PtTe as an interesting example of a cleavable, topological, and superconducting material.