In this Letter, we present the Advanced Satellite for Cosmology and Astrophysics data from EXO 0748-676 that indicate that a previously unnoted soft X-ray excess exists in the spectrum of this source.We have modeled the intensity-selected spectra with typical candidate low-mass X-ray binary spectral models. As expected, the best performing model was the generalized thermal (GT) model and an additional component that is thought to arise from the obscuration of the X-ray radiator by dipping material within the system. The GT model, however, has an unacceptable value of χ2ν (=3.16). We find that a previously undetected soft component exists (0.4-1.5 keV) in all intensity-selected data, which is the cause of the large value of χ2ν in our GT model fits. We modeled the new soft excess by adding an additional component to the GT model. A variety of soft component models were examined, and the best fitting was a steep power law with one or two local components (either edges or Gaussian lines), with the number of local components needed being dependent on the intensity-selected spectrum being fit. An edge feature and power-law model best fitted the quiescent soft spectral component, while Gaussian-line and power-law models best fitted the soft spectral component in all dipping spectra. We evaluate these results in terms of the expected physical geometry of this system.