We confirm that the object DDO216-A1 is a substantial globular cluster at the center of Local Group galaxy DDO216 (the Pegasus dwarf irregular), using Hubble Space Telescope ACS imaging. By fitting isochrones, we find the cluster metallicity to be [M/H] = -1.6 +/-0.2, for reddening E(B-V) = 0.16 +/-0.02; the best-fit age is 12.3 +/-0.8 Gyr. There are ~30 RR Lyrae variables in the cluster; the magnitude of the fundamental mode pulsators gives a distance modulus of 24.77 +/-0.08 - identical to the host galaxy. The ratio of overtone to fundamental mode variables and their mean periods make DDO216-A1 an Oosterhoff Type I cluster. We find an I-band central surface brightness 20.85 +/-0.17 F814W mag per square arcsecond, a half-light radius of 3.1 arcsec (13.4 pc), and an absolute magnitude M814 = -7.90 +/-0.16 (approximately 10^5 solar masses). King models fit to the cluster give the core radius and concentration index, r_c = 2.1 +/-0.9 and c = 1.24 +/-0.39. The cluster is an extended cluster somewhat typical of some dwarf galaxies and the outer halo of the Milky Way. The cluster is projected <30 pc south of the center of DDO216, unusually central compared to most dwarf galaxy globular clusters. Analytical models of dynamical friction and tidal destruction suggest that it probably formed at a larger distance, up to ~1 kpc, and migrated inward. DDO216 has an unexceptional cluster specific frequency, S_N = 10. DDO216 is the lowest-luminosity Local Group galaxy to host a 10^5 solar mass globular cluster, and the only transition-type (dSph/dIrr) in the Local Group with a globular.
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