The Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) was a multi-cycle treasury program on the Hubble Space Telescope (HST) that surveyed a total area of ~0.25 deg^2 with ~900 HST orbits spread across 5 fields over 3 years. Within these survey images we discovered 65 supernovae (SN) of all types, out to z~2.5. We classify ~24 of these as Type Ia SN (SN Ia) based on host-galaxy redshifts and SN photometry (supplemented by grism spectroscopy of 6 SN). Here we present a measurement of the volumetric SN Ia rate as a function of redshift, reaching for the first time beyond z=2 and putting new constraints on SN Ia progenitor models. Our highest redshift bin includes detections of SN that exploded when the universe was only ~3 Gyr old and near the peak of the cosmic star-formation history. This gives the CANDELS high-redshift sample unique leverage for evaluating the fraction of SN Ia that explode promptly after formation (<500 Myr). Combining the CANDELS rates with all available SN Ia rate measurements in the literature we find that this prompt SN Ia fraction is fP=0.53 +0.09 -0.10 (stat) +0.10 -0.26 (sys), consistent with a delay time distribution that follows a simple t^{-1} power law for all times t>40 Myr. However, a mild tension is apparent between ground-based low-z surveys and space-based high-z surveys. In both CANDELS and the sister HST program CLASH, we find a low rate of SN Ia at z>1. This could be a hint that prompt progenitors are in fact relatively rare, accounting for only ~20% of all SN Ia explosions -- though further analysis and larger samples will be needed to examine that suggestion.
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