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We report the development of a CaMoO4 crystal low temperature detector for the AMoRE neutrinoless double beta decay (0νββ) search experiment. The prototype detector cell was composed of a 216 g CaMoO4 crystal and a metallic magnetic calorimeter. An over-ground measurement demonstrated FWHM resolution of 6-11 keV for full absorption gamma peaks. Pulse shape discrimination was clearly demonstrated in the phonon signals, and 7.6 σ of discrimination power was found for the α and β/γ separation. The phonon signals showed rise-times of about 1 ms. It is expected that the relatively fast rise-time will increase the rejection efficiency of two-neutrino double beta decay pile-up events which can be one of the major background sources in 0νββ searches.