We present a pilot study of Galactic globular cluster (GC) proper motion (PM) determinations using Gaia data. We search for GC stars in the
Tycho-Gaia Astrometric Solution (TGAS) catalog from Gaia Data Release 1 (DR1), and identify five members of NGC 104 (47 Tucanae), one member
of NGC 5272 (M3), five members of NGC 6121 (M4), seven members of NGC 6397, and two members of NGC 6656 (M22). By taking a weighted average
of member stars, fully accounting for the correlations between parameters, we estimate the parallax (and, hence, distance) and PM of the GCs.
This provides a homogeneous PM study of multiple GCs based on an astrometric catalog with small and well-controlled systematic errors and
yields random PM errors similar to existing measurements. Detailed comparison to the available Hubble Space Telescope (HST) measurements
generally shows excellent agreement, validating the astrometric quality of both TGAS and HST. By contrast, comparison to ground-based
measurements shows that some of those must have systematic errors exceeding the random errors. Our parallax estimates have uncertainties
an order of magnitude larger than previous studies, but nevertheless imply distances consistent with previous estimates. By combining our
PM measurements with literature positions, distances, and radial velocities, we measure Galactocentric space motions for the clusters and
find that these also agree well with previous analyses. Our analysis provides a framework for determining more accurate distances and PMs
of Galactic GCs using future Gaia data releases. This will provide crucial constraints on the near end of the cosmic distance ladder and
provide accurate GC orbital histories.