We present an analysis of archival HST/ACS imaging in the F475W (g 475), F606W (V 606), and F814W (I 814) bands of the globular cluster (GC) system of a large (3.4 kpc effective radius) ultra-diffuse galaxy (DF17) believed to be located in the Coma Cluster of galaxies. We detect 11 GCs down to the 5σ completeness limit of the imaging (I 814 = 27 mag). Correcting for background and our detection limits yields a total population of GCs in this galaxy of 27 ± 5 and a V-band specific frequency S N = 28 ± 5. Based on comparisons to the GC systems of local galaxies, we show that both the absolute number and the colors of the GC system of DF17 are consistent with the GC system of a dark-matter-dominated dwarf galaxy with virial mass ∼9.0 × 1010 M ⊙ and a dark-to-stellar mass ratio M vir/M star ∼ 1000. Based on the stellar mass growth of the Milky Way, we show that DF17 cannot be understood as a failed Milky-Way-like system, but is more similar to quenched Large-Magellanic-Cloud-like systems. We find that the mean color of the GC population, g 475–I 814 = 0.91 ± 0.05 mag, coincides with the peak of the color distribution of intracluster GCs and is also similar to those of the blue GCs in the outer regions of massive galaxies. We suggest that both the intracluster GC population in Coma and the blue peak in the GC populations of massive galaxies may be fed—at least in part—by the disrupted equivalents of systems such as DF17.