Because of its proximity and its youth, the Pleiades open cluster of stars has been extensively studied and serves as a cornerstone for our understanding of the physical properties of young stars. This role is called into question by the "Pleiades distance controversy," wherein the cluster distance of 120.2 +/- 1.5 parsecs (pc) as measured by the optical space astrometry mission Hipparcos is significantly different from the distance of 133.5 +/- 1.2 pc derived with other techniques. We present an absolute trigonometric parallax distance measurement to the Pleiades cluster that uses very long baseline radio interferometry (VLBI). This distance of 136.2 +/- 1.2 pc is the most accurate and precise yet presented for the cluster and is incompatible with the Hipparcos distance determination. Our results cement existing astrophysical models for Pleiades-age stars.