Slow and fast light, or large changes in the group velocity of light, have been observed in a range of optical media, but the fine optical control necessary to induce an observable effect has not been achieved in a plasma. Here, we describe how the ion-acoustic response in a fully ionized plasma can produce large and measurable changes in the group velocity of light. We show the first experimental demonstration of slow and fast light in a plasma, measuring group velocities between 0.12c and -0.34c.