ß

For the first time, the (d,^{2}He) reaction was successfully used in inverse kinematics to extract the Gamow-Teller transition strength in the ß^{+} direction from an unstable nucleus. The new technique was made possible by the use of an active-target time-projection chamber and a magnetic spectrometer, and opens a path to addressing a range of scientific challenges, including in astrophysics and neutrino physics. In this Letter, the nucleus studied was ^{14}O, and the Gamow-Teller transition strength to ^{14}N was extracted up to an excitation energy of 22 MeV. The data were compared to shell-model and state-of-the-art coupled-cluster calculations. Shell-model calculations reproduce the measured Gamow-Teller strength distribution up to about 15 MeV reasonably well, after the application of a phenomenological quenching factor. In a significant step forward to better understand this quenching, the coupled-cluster calculation reproduces the full strength distribution well without such quenching, owing to the large model space, the inclusion of strong correlations, and the coupling of the weak interaction to two nucleons through two-body currents.