  We provide a consistent and complete calculation of the electric dipole
moments of the deuteron, helion, and triton in the framework of chiral
effective field theory. The CP-conserving and CP-violating interactions are
treated on equal footing and we consider CP-violating one-, two-, and
three-nucleon operators up to next-to-leading-order in the chiral power
counting. In particular, we calculate for the first time EDM contributions
induced by the CP-violating three-pion operator. We find that effects of
CP-violating nucleon-nucleon contact interactions are larger than those found
in previous studies based on phenomenological models for the CP-conserving
nucleon-nucleon interactions. Our results which apply to any model of CP
violation in the hadronic sector can be used to test various scenarios of CP
violation. As examples, we study the implications of our results on the QCD
$\theta$-term and the minimal left-right symmetric model.
