  The recent gravitational wave observations provide insight into the extreme
gravity regime of coalescing binaries, where gravity is strong, dynamical and
non-linear. The interpretation of these observations relies on the comparison
of the data to a gravitational wave model, which in turn depends on the orbital
evolution of the binary, and in particular on its orbital energy and angular
momentum decay. In this paper, we calculate the latter in the inspiral of a
non-spinning compact binary system within Einstein-\AE{}ther theory. From the
theory's gravitational wave stress energy tensor and a balance law, we compute
the angular momentum decay both as a function of the fields in the theory and
as a function of the multipole moments of the binary. We then specialize to a
Keplerian parameterization of the orbit to express the angular momentum decay
as a function of the binary's orbital elements. We conclude by combining this
with the orbital energy decay to find expressions for the decay of the
semi-major axis and the orbital eccentricity of the binary. We find that these
rates of decay are typically faster in Einstein-\AE{}ther theory than in
General Relativity due to the presence of dipole radiation. Such modifications
will imprint onto the chirp rate of gravitational waves, leaving a signature of
Einstein-\AE{}ther theory that if absent in the data could be used to
stringently constrain it.
