We use the Gaia data release 1 (DR1) to study the proper motion (PM) fields of the Large and Small Magellanic Clouds (LMC, SMC). This uses the Tycho-Gaia Astrometric Solution (TGAS) PMs for 29 Hipparcos stars in the LMC and 8 in the SMC. The LMC PM in the West and North directions is inferred to be $(mu_W,mu_N) = (-1.872 pm 0.045, 0.224 pm 0.054)$ mas/yr, and the SMC PM $(mu_W,mu_N) = (-0.874 pm 0.066, -1.229 pm 0.047)$ mas/yr. These results have similar accuracy and agree to within the uncertainties with existing Hubble Space Telescope (HST) PM measurements. Since TGAS uses different methods with different systematics, this provides an external validation of both data sets and their underlying approaches. Residual DR1 systematics may affect the TGAS results, but the HST agreement implies this must be below the random errors. Also in agreement with prior HST studies, the TGAS LMC PM field clearly shows the clockwise rotation of the disk, even though it takes the LMC disk in excess of $10^8$ years to complete one revolution. The implied rotation curve amplitude for young LMC stars is consistent with that inferred from line-of-sight (LOS) velocity measurements. Comparison of the PM and LOS rotation curves implies a kinematic LMC distance modulus $m-M = 18.54 pm 0.39$, consistent but not yet competitive with photometric methods. These first results from Gaia on the topic of Local Group dynamics provide an indication of how its future data releases will revolutionize this field.
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