We present a Chandra X-ray observation of the X-ray bright E2 elliptical galaxy NGC 4649. In addition to bright diffuse emission, we resolve 165 discrete sources, most of which are presumably low-mass X-ray binaries. As found in previous studies, the luminosity function of the resolved sources is well-fitted by a broken power law. In NGC 4697 and NGC 1553, the break luminosity was comparable to the Eddington luminosity of a 1.4 M-. neutron star. One possible interpretation of this result is that those sources with luminosities above the break are accreting black holes and those below are mainly accreting neutron stars. The total X-ray spectrum of the resolved sources is well fitted by a hard power law, while the diffuse spectrum requires a hard and a soft component, presumably due to the relatively soft diffuse gas and the harder unresolved sources. We also find evidence for structure in the diffuse emission near the center of NGC 4649. Specifically, there appear to be bright "fingers'' of emission extending from the center of the galaxy and a 500 long bar at the center of the galaxy. The fingers are morphologically similar to radial features seen in two-dimensional hydrodynamic simulations of cooling flows in elliptical galaxies, and although their other properties do not match the predictions of the particular simulations used, we conclude that the radial fingers might be due to convective motions of hot outflowing gas and cooler inflowing gas. The bar is coincident with the central extended radio source; we conclude that the bar may be caused by weak shocks in the diffuse gas from an undetected low-luminosity active galactic nucleus.