Ultra diffuse galaxies (UDGs) have the sizes of giant galaxies 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 $v_{rm sys}$ = 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 $(4.5 pm 2.8)times10^{9}$ $M_{odot}$ 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 $sim8times10^{10}$ $M_{odot}$, yielding a dark-to-stellar mass fraction of $sim3000$. We show that this UDG is an outlier in $M_{rm star} - M_{rm halo}$ 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.
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