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A scenario is proposed that explains both the observed high pulsar velocitiesand extragalactic gamma-ray bursts (GRBs). The model involves an ultra-relativistic jet from a supernova (SN), that produces a GRB and its afterglow,whose characteristics are similar to an isotropic fireball GRB perhaps withsome differences at late times in the afterglow once some significanttransverse diffusion has occurred. The time scales and many other properties ofGRBs and their afterglows in this model are consistent with observations.  GRBs in this model have special intrinsic properties, that can either falsifyor prove this model unambiguously by observations. The most direct proof is thedetection of a SN about the same time as the luminous GRB event. Most GRBs andSNe are expected occur at moderate redshift ($z\sim 1-3$), if they follow theobserved universal star formation history, as implied in this model. Searchingfor GRB/SN associations is a challenge, because majority of the SNe will befaint. Some additional, dramatic observable consequences are predicted, whichcan also be utilized to test the model.Comment: ApJ Letters in press, 4 emulateapj page

Supernovae, Pulsars, and Gamma-Ray Bursts: A Unified Picture