Ultra diffuse galaxies (UDGs) have the sizes of giants but the luminosities of dwarfs. A key to understanding their origins comes from their total masses, but their low surface brightnesses (mu > 25.0) generally prohibit dynamical studies. Here we report the first such measurements for a UDG (VCC 1287 in the Virgo cluster), based on its globular cluster system dynamics and size. From 7 GCs we measure a mean systemic velocity Vsys = 1071(-15+14) km/s, thereby confirming a Virgo-cluster association. We measure a velocity dispersion of 33(-10+16) km/s within 8.1 kpc, corresponding to an
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