  We report on a new measurement of the CP-violating permanent Electric Dipole
Moment (EDM) of the neutral $^{129}$Xe atom. Our experimental approach is based
on the detection of the free precession of co-located nuclear spin-polarized
$^3$He and $^{129}$Xe samples. The EDM measurement sensitivity benefits
strongly from long spin coherence times of several hours achieved in diluted
gases and homogeneous weak magnetic fields of about 400~nT. A finite EDM is
indicated by a change in the precession frequency, as an electric field is
periodically reversed with respect to the magnetic guiding field. Our result,
$\left(-4.7\pm6.4\right)\cdot 10^{-28}$ ecm, is consistent with zero and is
used to place a new upper limit on the $^{129}$Xe EDM: $|d_\text{Xe}|<1.5 \cdot
10^{-27}$ ecm (95% C.L.). We also discuss the implications of this result for
various CP-violating observables as they relate to theories of physics beyond
the standard model.
