We used the Chandra X-Ray Observatory ACIS-S3 to image the X-ray-faint elliptical galaxy NGC 4365 and lenticular galaxy NGC 4382. The observations resolve much of the X-ray emission into 99 and 58 sources, respectively, most of which are low-mass X-ray binaries (LMXBs) associated with each of the galaxies. Within one effective radius of NGC 4365, about 45% of the counts are resolved into sources, 30% are attributed to unresolved LMXBs, and 25% are attributed to diffuse gas. Within two effective radii of NGC 4382, about 22% of the counts are resolved into sources, 33% are attributed to unresolved LMXBs, and 45% are attributed to diffuse gas. We identify 18 out of the 37 X-ray sources in a central field in NGC 4365 with globular clusters.