We describe the first precision measurement of the electron's electric dipole moment (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 [3][4][5][6][7][8][9].The most precise eEDM measurements to date were performed using beams of neutral atoms or molecules [3][4][5]. These experiments benefited from excellent statistical sensitivity provided by a high flux of neutral particles, and decades of past work have produced a thorough understanding of their common sources of systematic error. Nonetheless, a crucial systematics check can be provided by independent measurements conducted using different physical systems and experimental techniques. Moreover, techniques that allow longer interrogation times offer significant potential for sensitivity improvements in eEDM searches and other tests of fundamental physics [10].In this Letter, we report on a precision measurement of the eEDM using molecular ions confined in a radio frequency (rf) [17] and our use of a rf trap allow us to attain spin precession times in excess of 700 ms-nearly 3 orders of magnitude longer than in contemporary neutral beam experiments. This exceptionally long interrogation time allows us to obtain high eEDM sensitivity despite our lower count rate. In addition, performing an experiment on trapped particles permits the measurement of spin precession fringes at arbitrary free-evolution times, making our experiment relatively immune to systematic errors associated with imperfectly characterized state preparation.Our apparatus and experimental sequence, shown schematically in Fig. 1, have been described previously [11,12,[17][18][19][20]. We produce HfF by ablation of Hf metal into a pulsed supersonic expansion of Ar and SF 6 . The neutral beam enters the rf trap, where HfF is ionized with pulsed UV lasers to form HfF þ in its ground vibronic state [18,19]. The ions are stopped by a pulsed voltage on the radial trap electrodes, then confined by dc and rf electric quadrupole gradients (with f rf ¼ 50 kHz). We next adiabatically turn on a spatially uniform electric bias field E rot ≈ 24 V=cm that rotates in the radial plane of the ion trap with frequency f rot ≈ 250 kHz, causing the ions to undergo circular motion with radius r rot ≈ 0.5 mm. A pair of magnet coils aligned with the Z axis produces an axial magnetic gradient B ¼ B 0 axgrad ð2Z − X − YÞ where jB 0 axgrad j ≈ 40 mG=cm, which in the rotating frame of the ions creates a magnetic bias field B rot ≡ jhB · E rot =E rot ij ≃ jB 0 axgrad r rot j that is parallel (antiparallel) to E rot if B 0 axgrad > 0 (<0) [11,12].Our state preparation consists of population transfer to the eEDM-sensitive 3 Δ 1 state and selective depletion of magnetic sublevels to produce a pure spin state [Figs. 1(b) and 1(c)]. Two continuous wave lasers copropagating along theẐ axis drive a Raman transition through a 119, 153001 (2017)