In anomaly-mediated supersymmetry breaking, superpartners in a hidden sector have masses that are proportional to couplings squared and so naturally freeze out with the desired dark matter relic density for a large range of masses. We present an extremely simple realization of this possibility, with WIMPless dark matter arising from a hidden sector that is supersymmetric QED with ${N}_{F}$ flavors. Dark matter is multicomponent, composed of hidden leptons and sleptons with masses anywhere from 10 GeV to 10 TeV, and hidden photons provide the thermal bath. The dark matter self-interacts through hidden sector Coulomb scatterings that are potentially observable. In addition, the hidden photon contribution to the number of relativistic degrees of freedom is in the range $\ensuremath{\Delta}{N}_{\mathrm{eff}}\ensuremath{\sim}0--2$, and, if the hidden and visible sectors were initially in thermal contact, the model predicts $\ensuremath{\Delta}{N}_{\mathrm{eff}}\ensuremath{\sim}0.2--0.4$. Data already taken by Planck may provide evidence of such deviations.