We present the first complete calculation of the history of the inhomogeneous 21-cm signal from neutral hydrogen during the era of the first stars. We use hybrid computational methods to capture the large-scale distribution of the first stars, whose radiation couples to the neutral hydrogen emission, and to evaluate the 21-cm signal from z ~ 15-35. In our realistic picture large-scale fluctuations in the 21-cm signal are sourced by the inhomogeneous density field and by the Ly-alpha and X-ray radiative backgrounds. The star formation is suppressed by two spatially varying effects: negative feedback provided by the Lyman-Werner radiative background, and supersonic relative velocities between the gas and dark matter. Our conclusions are quite promising: we find that the fluctuations imprinted by the inhomogeneous Ly-alpha background in the 21-cm signal at z ~ 25 should be detectable with the Square Kilometer Array.