Using the Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST), we have obtained a direct trigonometric parallax for the nearest metal-poor globular cluster, NGC 6397. Although trigonometric parallaxes have been previously measured for many nearby open clusters, this is the first parallax for an ancient metal-poor population -- one that is used as a fundamental template in many stellar population studies. This high-precision measurement was enabled by the HST/WFC3 spatial-scanning mode, providing hundreds of astrometric measurements for dozens of stars in the cluster and also for Galactic field stars along the same sightline. We find a parallax of 0.418 +/- 0.013 +/- 0.018 mas (statistical, systematic), corresponding to a true distance modulus of 11.89 +/- 0.07 +/- 0.09 mag (2.39 +/- 0.07 +/- 0.10 kpc). The V luminosity at the stellar main sequence turnoff implies an absolute cluster age of 13.4 +/- 0.7 +/- 1.2 Gyr.