Chandra observations of the X-ray-faint elliptical galaxy NGC 4697 resolve much of the X-ray emission (61% within one effective radius) into similar to 80 point sources, of which most are low-mass X-ray binaries (LMXBs). These LMXBs provide the bulk of the hard emission and much of the soft emission as well. Of the remaining unresolved emission, it is likely that about half is from fainter LMXBs, while the other half (similar to 23% of the total emission) is from interstellar gas. Three of the resolved sources are supersoft sources. In the outer regions of NGC 4697, eight of the LMXBs (about 25%) are coincident with candidate globular clusters, indicating that globulars have a high probability of containing X-ray binaries compared with the normal stellar population. The X-ray luminosities (0.3-10 keV) of the resolved LMXBs range from similar to5 x 10(37) to similar to2.5 x 10(39) ergs s(-1). The luminosity function of the LMXBs has a "knee" at 3.2 x 10(38) ergs s(-1), which is roughly the Eddington luminosity of an 1.4 M-. neutron star (NS); this knee might be useful as a distance indicator. The highest luminosity source has the Eddington luminosity of an similar to 20 M-. black hole (BH). The presence of this large population of NS and massive BH stellar remnants in this elliptical galaxy shows that it (or its progenitors) once contained a large population of massive main-sequence stars.