We describe a new technique to measure the EDM of $^{129}$Xe with $^3$He comagnetometry. Both species are polarized using spin-exchange optical pumping, transferred to a measurement cell, and transported into a magnetically shielded room, where SQUID magnetometers detect free precession in applied electric and magnetic fields. The result of a one week run combined with a detailed study of systematic effects is $d_A(^{129}mathrm{Xe}) = (0.26 pm 2.33_mathrm{stat} pm 0.72_mathrm{syst})times10^{-27}~e,mathrm{cm}$. This corresponds to an upper limit of $|d_A(^{129}mathrm{Xe})| < 4.81times 10^{-27} ~e,mathrm{cm}~(95%~mathrm{CL})$, a factor of 1.4 more sensitive than the previous limit.
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