We present a study of the X-ray emission from the nuclei of galaxies observed in the core of the Perseus cluster in a deep exposure with Chandra. Point sources are found coincident with the nuclei of 13 early-type galaxies, as well as the central galaxy NGC1275. This corresponds to all galaxies brighter than MB> -18 in the Chandra field. All of these sources have a steep power-law spectral component and four have an additional thermal component. The unabsorbed power-law luminosities in the 0.5-7.0 keV band range from 8x1038 to 5x1040erg/s. We find no simple correlations between the K-band luminosity, or the FUV and NUV AB magnitudes of these galaxies and their X-ray properties. We have estimated the black hole masses of the nuclei using the K-band MBH-L_Kbol_ relation and again find no correlation between black hole mass and the X-ray luminosity. Bondi accretion on to the black holes in the galaxies with minihaloes should make them much more luminous than observed.