  In this paper, we introduce 3-Hom-Lie bialgebras whose compatibility
conditions between the multiplication and comultiplication are given by local
cocycle conditions. We study a twisted 3-ary version of the Yang-Baxter
Equation, called the 3-Lie classical HomYang-Baxter Equation (3-Lie CHYBE),
which is a general form of 3-Lie classical YangBaxter Equation studied in [2]
and prove that the bialgebras induced by the solutions of 3-Lie CHYBE induce
the coboundary local cocycle 3-Hom-Lie bialgebras.
