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We have recently started to develop a high-resolution gamma-ray spectrometer for material defect analysis. Our gamma-ray detector is a microcalorimeter consisting of an iridium/gold bilayer transition edge sensor (TES) thermometer and a bulk Pb absorber, which is directly coupled to a TES with Stycast 2850FT epoxy. This paper describes our TES based gamma-ray detector and the first experimental results for 662 keV and 1173 keV incident gamma-rays. We report an energy resolution of 4.7 keV at 662 keV and 2.9 keV at 1173 keV.