  Chern-Simons modified gravity is a string-theory and loop-quantum-gravity
inspired effective theory that modifies General Relativity by adding a
parity-violating Pontryagin density to the Einstein-Hilbert action multiplied
by a coupling scalar. We strongly constrain non-dynamical Chern-Simons modified
gravity with a timelike Chern-Simons scalar through observations of the double
binary pulsar PSR J0737-3039A/B. We first calculate Chern-Simons corrections to
the orbital evolution of binary systems. We find that the ratio of the
correction to periastron precession to the general relativistic prediction
scales quadratically with the semi-major axis and inversely with the square of
the object's radius. Binary pulsar systems are thus ideal to test this theory,
since periastron precession can be measured with sub-degree accuracies and the
semi-major axis is millions of times larger than the stellar radius. Using data
from PSR J0737-3039A/B we dramatically constrain the non-dynamical Chern-Simons
coupling to $M_{\CS} := 1/|\dot{\vartheta}| > 33 {\textrm{meV}}$, approximately
a hundred billion times better than current Solar System tests.
