  The best limit on the electron electric dipole moment (eEDM) comes from the
ACME II experiment [Nature \textbf{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.
