  Having great accuracy in the range and range rate measurements,he GRACE
mission and the planed GRACE Follow On mission can in principle be employed to
place strong constraints on certain relativistic gravitational theories. In
this paper, we work out the range observable of the non-dynamical Chern-Simons
modified gravity for the Satellite-to-Satellite Tracking (SST) measurements. We
find out that a characteristic time accumulating range signal appears in
non-dynamical Chern-Simons gravity, which has no analogue found in the standard
parity-preserving metric theories of gravity. The magnitude of this
Chern-Simons range signal will reach a few times of $\chi cm$ for each free
flight of these SST missions, here $\chi$ is the dimensionless post-Newtonian
parameter of the non-dynamical Chern-Simons theory. Therefore, with the 12
years data of the GRACE mission, one expects that the mass scale
$M_{CS}=\frac{4\hbar c}{\chi a}$ of the non-dynamical Chern-Simons gravity
could be constrained to be larger than $1.9\times10^{-9}eV$. For the GRACE FO
mission that scheduled to be launched in 2017, the much stronger bound that
$M_{CS}\geq5\times10^{-7}eV$ is expected.
