We present an analysis of Chandra observations of the position of 10 nearby (<25Mpc) Type Ia supernovae, taken before the explosions. No sources corresponding to progenitors were found in any of the observations. We calculated upper limits on the bolometric luminosities of the progenitors assuming blackbody X-ray spectra with temperatures of 30-150eV. This is inspired by the fact that luminous super-soft X-ray sources have been suggested as the direct progenitors of Type Ia supernovae. The upper limits of two supernovae in our sample are comparable to the luminosities of the brightest observed super-soft sources, ruling out such sources as the progenitors of these supernovae. In contrast to Liu et al. (2012ApJ...749..141L), we find that for SN2011fe we can rule out Eddington luminosity systems for blackbody temperatures as low as 40eV. Our findings are consistent with statistical studies comparing the observed Type Ia supernova rate to the number of super-soft sources or the integrated X-ray luminosity in external galaxies. This suggests that either the progenitors of Type Ia supernovae are not accreting, nuclear burning white dwarfs or that they do not look like the classical super-soft sources, e.g. because they are obscured.