Ytterbium (Yb) metal is divalent and nonmagnetic (4f14 configuration). Under pressure its valence increases significantly leading to the expectation that magnetic instabilities and other highly correlated electron effects may appear before a stable trivalent state is reached (4f13 configuration). We carried out electrical resistivity and ac magnetic susceptibility measurements to 179 GPa over the temperature range 1.4-295 K. No evidence for magnetic order is observed. However, Yb becomes a superconductor at 86 GPa with Tc≃1.4 K, increasing to 4.6 K at 179 GPa. X-ray absorption spectroscopy shows that Yb remains mixed valent to at least 125 GPa, pointing to an active role of f electrons in the emergence of superconductivity in this simple, elemental solid.