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In this paper, an amplifier with a significant amount of gain is demonstrated at sub-millimeter wave frequencies (f > 300-GHz) for the first time. The three stage amplifier uses advanced InP HEMT transistors to realize 16-dB gain at 340-GHz and > 20 dB gain at 280-GHz. The amplifier demonstrates > 100 GHz of bandwidth with gain > 10 dB. This paper demonstrates that full WR-3 waveguide band (220-325 GHz) InP HEMT amplifiers are currently possible and that current device capabilities enable operation well into the sub-millimeter wave regime.