The first locations of short gamma-ray bursts (GRBs) in elliptical galaxies suggest they are produced by the mergers of double neutron star (DNS) binaries in old stellar populations. Globular clusters, where the extreme densities of very old stars in cluster cores create and exchange compact binaries efficiently, are a natural environment to produce merging NSs. They also allow some short GRBs to be offset from their host galaxies, as opposed to DNS systems formed from massive binary stars which appear to remain in galactic disks. Starting with a simple scaling from the first DNS observed in a galactic globular, which will produce a short GRB in ~300My, we present numerical simulations which show that ~10-30% of short GRBs may be produced in globular clusters vs. the much more numerous DNS mergers and short GRBs predicted for galactic disks. Reconciling the rates suggests the disk short GRBs are more beamed, perhaps by both the increased merger angular momentum from the DNS spin-orbit alignment (random for the DNS systems in globulars) and a larger magnetic field on the secondary NS.