We describe the first precision measurement of the electrons 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.