We have developed ultralow-noise electronics in combination with repetitive, nondestructive readout of a thick, fully depleted charge-coupled device (CCD) to achieve an unprecedented noise level of 0.068 e- rms/pixel. This is the first time that discrete subelectron readout noise has been achieved reproducible over millions of pixels on a stable, large-area detector. This enables the contemporaneous, discrete, and quantized measurement of charge in pixels, irrespective of whether they contain zero electrons or thousands of electrons. Thus, the resulting CCD detector is an ultra-sensitive calorimeter. It is also capable of counting single photons in the optical and near-infrared regime. Implementing this innovative non-destructive readout system has a negligible impact on CCD design and fabrication, and there are nearly immediate scientific applications. As a particle detector, this CCD will have unprecedented sensitivity to low-mass dark matter particles and coherent neutrino-nucleus scattering, while future astronomical applications may include direct imaging and spectroscopy of exoplanets.