We present the results of a search for nuclear X-ray activity in nearby galaxies using Chandra archival data in a sample of 62 galaxies from the Spitzer Infrared Nearby Galaxy Survey (SINGS). We detect 37 nuclear X-ray sources; seven of these are new detections. Most of the nuclear X-ray sources are likely to be AGNs. The fraction of galaxies hosting AGNs is thus about 60%, much higher than that found with optical searches, and demonstrates the efficacy of X-ray observations to find hidden AGNs in optically normal galaxies. We find that the nuclear X-ray sources are preferentially present in earlier type galaxies. Unlike what is observed at high redshift, we do not find a strong correlation between the AGN luminosity and the 24 micron luminosity of the host galaxy; we find a strong correlation with the 3.6 micron luminosity instead. This suggests that at the present epoch the accretion rate depends on the total mass of the galaxy, as perhaps does the black hole mass.