CCDs are getting pretty good these days, but all systems are subject to noise. A typical value for a CCD seems to be 20 electrons RMS per pixel. This article from qsimaging.com says
CCD Read Noise is a fundamental trait of CCDs, from the one in an inexpensive webcam to the CCDs in the Hubble Space Telescope. CCD read noise ultimately limits a camera’s signal to noise ratio, but as long as this noise exhibits a Gaussian, or normal distribution, its influence on your images can be reduced by combining frames and standard image processing techniques.
It doesn't really describe the source of the noise however. I know that astronomers like to cool their CCDs, so I'm thinking it is from thermal phonons being converted to electrons? I'm specifically asking about the CCD so lets assume that the shot noise of the incoming light is well below the typical CCD noise quoted above.