Superfluidity is a macroscopic quantum phenomenon occurring in systems as diverse as liquid helium and neutron stars. It occurs below a critical temperature(1,2) and leads to peculiar behaviour such as frictionless flow, the formation of quantized vortices and quenching of the moment of inertia. Ultracold atomic gases offer control of interactions and external confinement, providing unique opportunities to explore superfluid phenomena. Many such (finite-temperature) phenomena can be explained in terms of a two-fluid mixture(3,4) comprising a normal component, which behaves like an ordinary fluid, and a superfluid component with zero viscosity and zero entropy. The two-component nature of a superfluid is manifest in 'second sound', an entropy wave in which the superfluid and the non-superfluid components oscillate with opposite phases (as opposed to ordinary 'first sound', where they oscillate in phase). Here we report the observation of second sound in an ultracold Fermi gas with resonant interactions. The speed of second sound depends explicitly on the value of the superfluid fraction(5), a quantity that is sensitive to the spectrum of elementary excitations(6). Our measurements allow us to extract the temperature dependence of the superfluid fraction, a previously inaccessible quantity that will provide a benchmark for theories of strongly interacting quantum gases.