The Baldwin, Phillips, and Terlevich emission-line ratio diagnostic ([OIII]/H{beta} versus [NII]/H{alpha}, hereafter BPT diagram) efficiently separates galaxies whose signal is dominated by star formation <BPT-SF> from those dominated by AGN activity (BPT-AGN). Yet this BPT diagram is limited to z < 0.5, the redshift at which [NII]{lambda}6584 leaves the optical spectral window. Using the Sloan Digital Sky Survey (SDSS), we construct a new diagnostic, or TBT diagram, that is based on rest-frame g-z color, [NeIII]{lambda}3869, and [OII]{lambda}{lambda}3726 + 3729 and can be used for galaxies out to z < 1.4. The TBT diagram identifies 98.7% of the SDSS BPT-AGN as TBT-AGN and 97% of the SDSS BPT-SF as TBT-SF. Furthermore, it identifies 97% of the OPTX Chandra X-ray selected AGNs as TBT-AGN. This is in contrast to the BPT diagram, which misidentifies 20% of X-ray selected AGNs as BPT-SF. We use the GOODS-N and Lockman Hole galaxy samples, with their accompanying deep Chandra imaging, to perform X-ray and infrared stacking analyses to further validate our TBT-AGN and TBT-SF selections; that is, we verify the dominance of AGN activity in the former and star formation activity in the latter. Finally, we address the inclusion of the majority of the BPT-comp (sources lying between the BPT-SF and BPT-AGN regimes) in our TBT-AGN regime. We find that the stacked BPT-comp source is X-ray hard (<{Gamma}eff> = 1.0 +/-0.4) and has a high X-ray luminosity to total infrared luminosity ratio. This suggests that, on average, the X-ray signal in BPT-comp is dominated by obscured or low accretion rate AGN activity rather than by star formation, supporting their inclusion in the TBT-AGN regime.
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