In an effort to measure the Rossiter-McLaughlin effect for the TRAPPIST-1 system, we performed high-resolution spectroscopy during transits of planets e, f, and b. The spectra were obtained with the InfraRed Doppler spectrograph on the Subaru 8.2-m telescope, and were supplemented with simultaneous photometry obtained with a 1-m telescope of the Las Cumbres Observatory Global Telescope. By analyzing the anomalous radial velocities, we found the projected stellar obliquity to be $lambda=1pm 28$ degrees under the assumption that the three planets have coplanar orbits, although we caution that the radial-velocity data show correlated noise of unknown origin. We also sought evidence for the expected deformations of the stellar absorption lines, and thereby detected the Doppler shadow of planet b with a false alarm probability of $1.7,%$. The joint analysis of the observed residual cross-correlation map including the three transits gave $lambda=19_{-15}^{+13}$ degrees. These results indicate that the the TRAPPIST-1 star is not strongly misaligned with the common orbital plane of the planets, although further observations are encouraged to verify this conclusion.
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