We characterize the response of a novel 250 $mu$m thick, fully-depleted Skipper Charged-Coupled Device (CCD) to visible/near-infrared light with a focus on potential applications for astronomical observations. We achieve stable, single-electron resolution with readout noise $sigma sim 0.18$ e$^{-}$ rms/pix from 400 non-destructive measurements of the charge in each pixel. We verify that the gain derived from photon transfer curve measurements agrees with the gain calculated from the quantized charge of individual electrons to within < 1%. We also perform relative quantum efficiency measurements and demonstrate high relative quantum efficiency at optical/near-infrared wavelengths, as is expected for a thick, fully depleted detector. Finally, we demonstrate the ability to perform multiple non-destructive measurements and achieve sub-electron readout noise over configurable subregions of the detector. This work is the first step toward demonstrating the utility of Skipper CCDs for future astronomical and cosmological applications.
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