  For an ergodic probability-measure-preserving action $G \curvearrowright (X,
\mu)$ of a countable group $G$, we define the Rokhlin entropy
$h_G^{\mathrm{Rok}}(X, \mu)$ to be the infimum of the Shannon entropies of
countable generating partitions. It is known that for free ergodic actions of
amenable groups this notion coincides with classical Kolmogorov--Sinai entropy.
It is thus natural to view Rokhlin entropy as a close analogue to classical
entropy. Under this analogy we prove that Krieger's finite generator theorem
holds for all countably infinite groups. Specifically, if
$h_G^{\mathrm{Rok}}(X, \mu) < \log(k)$ then there exists a generating partition
consisting of $k$ sets.
