We report results of a new technique to measure the electric dipole moment 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 from a one week measurement campaign in 2017 and a 2.5 week campaign in 2018, combined with detailed study of systematic effects, is $d_A(^{129}mathrm{Xe}) = (1.4 pm 6.6_mathrm{stat} pm 2.0_mathrm{syst})times10^{-28}~e,mathrm{cm}$. This corresponds to an upper limit of $|d_A(^{129}mathrm{Xe})| < 1.4 times 10^{-27} ~e,mathrm{cm}~(95%~mathrm{CL})$, a factor of five more sensitive than the limit set in 2001.
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