Ytterbium (Yb) metal is divalent and nonmagnetic (4f^{14} 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 (4f^{13} 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 T_{c}≃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.