  We explore the feasibility and astrophysical consequences of a new long-range
U(1) gauge field ("dark electromagnetism") that couples only to dark matter,
not to the Standard Model. The dark matter consists of an equal number of
positive and negative charges under the new force, but annihilations are
suppressed if the dark matter mass is sufficiently high and the dark
fine-structure constant $\hat\alpha$ is sufficiently small. The correct relic
abundance can be obtained if the dark matter also couples to the conventional
weak interactions, and we verify that this is consistent with particle-physics
constraints. The primary limit on $\hat\alpha$ comes from the demand that the
dark matter be effectively collisionless in galactic dynamics, which implies
$\hat\alpha \lesssim 10^{-4}$ for TeV-scale dark matter. These values are
easily compatible with constraints from structure formation and primordial
nucleosynthesis. We raise the prospect of interesting new plasma effects in
dark matter dynamics, which remain to be explored.
