Permanent electric dipole moment (EDM) measurements of ^{129}Xe, along with other diamagnetic systems and the neutron, constrain beyond-the-standard-model hadronic CP-violating parameters. In the HeXeEDM experiment, a new technique is used to measure the EDM of ^{129}Xe with a ^3He comagnetometer and has potential to improve the current limit by two orders of magnitude. ^3He and ^{129}Xe are polarized using spin-exchange optical pumping, transferred to a measurement cell and then transported into a magnetically shielded room. The free precession of both species is detected in the presence of an applied 3 kV/cm electric field and a 2.6 muT magnetic field using SQUID magnetometers.