We report on the population of point sources discovered during an 18.5ks Chandra ACIS-S observation of the Sombrero galaxy. We present the luminosity function and the spectra of the six brightest sources, consider correlations with globular clusters (GCs) and with planetary nebulae, and study the galaxy's population of very soft sources. We detected 122 sources. Twenty-two sources are identified as very soft; of these, five appear to be classical luminous supersoft X-ray sources (SSSs), while 17 may belong to the slightly harder class referred to as quasi-soft (QSSs). There is an overdensity of very soft sources within 2kpc of the nucleus, which is itself the brightest X-ray source. Very soft sources are also found in the disk and halo, with one QSS in a globular cluster (GC).