  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.
