The best limit on the electron electric dipole moment (eEDM) comes from the ACME II experiment [Nature 562 (2018), 355-360] which probes physics beyond the Standard Model at energy scales well above 1 TeV. ACME II measured the eEDM by monitoring electron spin precession in a cold beam of the metastable H$^3\Delta_1$ state of thorium monoxide (ThO) molecules, with an observation time $\tau \approx 1$ ms for each molecule. We report here a new measurement of the lifetime of the ThO (H$^3\Delta_1$) state, $\tau_H = 4.2\pm 0.5$ ms. Using an apparatus within which $\tau \approx \tau_H$ will enable a substantial reduction in uncertainty of an eEDM measurement.