An equivalence relation E on a Polish space X is classifiable by a Polish group G if there is a Borel reduction from E to the orbit equivalence relation of some continuous action of G on a Polish space. A countable Borel equivalence relation (CBER) is an equivalence relation on a Polish space which is Borel (as a set of pairs) and such that all of its equivalence classes are countable. Of particular interest is the class of hyperfinite CBERs, that is, those which are classified by the group of integers. It is known that a CBER is hyperfinite if it is classified by a locally compact Polish abelian group, and Hjorth conjectured that this should hold for any Polish abelian group. Recently, Allison refuted this conjecture by showing that every treeable CBER is classified by a Polish abelian group (there are treeable CBERs which are not hyperfinite, such as the free part of the Bernoulli shift of a non-abelian free group). We extend Allison's methods to show that in fact, every CBER is classified by a Polish abelian group. This is joint with Josh Frisch.