  We describe the first precision measurement of the electron's electric dipole
moment (eEDM, $d_e$) using trapped molecular ions, demonstrating the
application of spin interrogation times over 700 ms to achieve high sensitivity
and stringent rejection of systematic errors. Through electron spin resonance
spectroscopy on $^{180}{\rm Hf}^{19}{\rm F}^{+}$ in its metastable
$^{3}\Delta_{1}$ electronic state, we obtain $d_e = (0.9 \pm 7.7_{\rm stat} \pm
1.7_{\rm syst}) \times 10^{-29}\,e\,{\rm cm}$, resulting in an upper bound of
$|d_e| < 1.3 \times 10^{-28}\,e\,{\rm cm}$ (90% confidence). Our result
provides independent confirmation of the current upper bound of $|d_e| < 9.3
\times 10^{-29}\,e\,{\rm cm}$ [J. Baron $\textit{et al.}$, Science
$\textbf{343}$, 269 (2014)], and offers the potential to improve on this limit
in the near future.
