We explore a scenario in which metal-poor globular clusters (GCs) are enriched by the first supernovae in the universe. If the first stars in a 107 Msolar dark halo were very massive (>180 Msolar), then a pair-instability supernova from a single massive star could produce sufficient iron to enrich 106 Msolar of pristine, primordial gas to [Fe/H]~-2. In such a scenario, in which a single massive star acts as a seed for halo GCs, an accurate abundance analysis of GC stars would allow us to directly measure the Population III initial mass. Using the latest theoretical yields for zero-metallicity stars in the mass range of 140-260 Msolar, we find that the metals expelled from an ~230 Msolar star are consistent with [Si/Fe] and [Ca/Fe] observed in GC stars. However, no single star in this mass range can simultaneously explain all halo GC heavy-element abundance ratios, such as [V/Fe], [Ti/Fe], and [Ni/Fe]. These require a combination of masses for the Population III stellar progenitors. The various observational consequences of this scenario are discussed.