(Abridged) We conducted a Chandra ACIS observation of the nearby Sculptor Group Sd galaxy NGC 7793. At the assumed distance to NGC 7793 of 3.91 Mpc, the limiting unabsorbed luminosity of the detected discrete X-ray sources (0.2-10.0 keV) is approximately 3x10^36 ergs s^-1. A total of 22 discrete sources were detected at the 3-sigma level or greater including one ultra-luminous X-ray source (ULX). Based on multiwavelength comparisons, we identify X-ray sources coincident with one SNR, the candidate microquasar N7793-S26, one HII region and two foreground Galactic stars. We also find that the X-ray counterpart to the candidate radio SNR R3 is time-variable in its X-ray emission: we therefore rule out the possibility that this source is a single SNR. A marked asymmetry is seen in the distribution of the discrete sources with the majority lying in the eastern half of this galaxy. All of the sources were analyzed using quantiles to estimate spectral properties and spectra of the four brightest sources (including the ULX) were extracted and analyzed. We searched for time-variability in the X-ray emission of the detected discrete sources using our measured fluxes along with fluxes measured from prior Einstein and ROSAT observations. From this study, three discrete X-ray sources are established to be significantly variable. A spectral analysis of the galaxys diffuse emission is characterized by a temperature of kT = 0.19-0.25 keV. The luminosity function of the discrete sources shows a slope with an absolute value of Gamma = -0.65+/-0.11 if we exclude the ULX. If the ULX is included, the luminosity function has a long tail to high L_X with a poor-fitting slope of Gamma = -0.62+/-0.2. The ULX-less slope is comparable to the slopes measured for the distributions of NGC 6946 and NGC 2403 but much shallower than the slopes measured for the distributions of IC 5332 and M83.
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