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 ( V ) \geq 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 v _ { sys } = 1071 ^ { +14 } _ { -15 } km/s , thereby confirming a Virgo-cluster association . We measure a velocity dispersion of 33 ^ { +16 } _ { -10 } km/s within 8.1 kpc , corresponding to an enclosed mass of ( 4.5 \pm 2.8 ) \times 10 ^ { 9 } M _ { \odot } and a g -band mass-to-light ratio of ( M / L ) _ { g } = 106 ^ { +126 } _ { -54 } . From the cumulative mass curve , along with the GC numbers , we estimate a virial mass of \sim 8 \times 10 ^ { 10 } M _ { \odot } , yielding a dark-to-stellar mass fraction of \sim 3000 . We show that this UDG is an outlier in M _ { star } – M _ { halo } relations , suggesting extreme stochasticity in relatively massive star-forming halos in clusters . Finally , we discuss how counting GCs offers an efficient route to determining virial masses for UDGs .