We present a model with dark matter in an anomaly-mediated supersymmetry breaking hidden sector with a U(1)×U(1) gauge symmetry. The symmetries of the model stabilize the dark matter and forbid the introduction of new mass parameters. As a result, the thermal relic density is completely determined by the gravitino mass and dimensionless couplings. Assuming nonhierarchical couplings, the thermal relic density is Ω X∼0.1, independent of the dark matter's mass and interaction strength, realizing the WIMPless miracle. The model has several striking features. For particle physics, stability of the dark matter is completely consistent with R-parity violation in the visible sector, with implications for superpartner collider signatures; also the thermal relic's mass may be ∼10GeV or lighter, which is of interest given recent direct detection results. Interesting astrophysical signatures are dark matter self-interactions through a long-range force, and massless hidden photons and fermions that contribute to the number of relativistic degrees of freedom at big bang nucleosynthesis and cosmic microwave background. The latter are particularly interesting, given current indications for extra degrees of freedom and near future results from the Planck observatory. © 2012 American Physical Society.