  Parity violation in gravity, if existed, could have important implications,
and it is meaningful to search and test the possible observational effects.
Chern-Simons modified gravity serves as a natural model for gravitational
parity-violations. Especially, considering extensions to Einstein-Hilbert
action up to second order curvature terms, it is known that theories of
gravitational parity-violation will reduce to the dynamical Chern-Simons
gravity. In this letter, we outline the theoretical principles of testing the
dynamical Chern-Simons gravity with orbiting gravity gradiometers, which could
be naturally incorporated into future satellite gravity missions. The secular
gravity gradient signals, due to the Mashhoon-Theiss (anomaly) effect, in
dynamical Chern-Simons gravity are worked out, which can improve the constraint
of the corresponding Chern-Simons length scale $\xi^{\frac{1}{4}}_{cs}$
obtained from such measurement scheme. For orbiting superconducting
gradiometers or gradiometers with optical readout, a bound
$\xi^{\frac{1}{4}}_{cs}\leq 10^6 \ km$ (or even better) could in principle be
obtained, which will be at least 2 orders of magnitude stronger than the
current one based on the observations from the GP-B mission and the LAGEOS I,
II satellites.
