We report the results of the Chandra observations of the Swift-discovered short gamma-ray burst GRB 050724. Chandra observed this burst twice, about 2 days after the burst and a second time 3 weeks later. The first Chandra pointing occurred at the end of a strong late-time flare. About 150 photons were detected during this 49.3 ks observation in the 0.4-10.0 keV range. The spectral fit is in good agreement with spectral analysis of earlier Swift XRT data. In the second Chandra pointing the afterglow was clearly detected with eight background-subtracted photons in 44.6 ks. From the combined Swift XRT and Chandra-ACIS-S light curve we find significant flaring superposed on an underlying power-law decay slope of α=0.98+0.11-0.09. There is no evidence for a break between about 1 ks after the burst and the last Chandra pointing about 3 weeks after the burst. The nondetection of a jet break places a lower limit of 25° on the jet opening angle, indicating that the outflow is less strongly collimated than most previously reported long GRBs. This implies that the beaming corrected energy of GRB 050724 is at least 4×1049 ergs.