We present a non-LTE model atmosphere analysis of Chandra HRC-S/LETG and XMM-Newton RGS spectroscopy of the prototypical supersoft source CAL 83 in the Large Magellanic Cloud. Taken with a 16-month interval, the Chandra and XMM-Newton spectra are very similar. They reveal a very rich absorption line spectrum from the hot white dwarf photosphere, but no spectral signatures of a wind. We also report a third X-ray off-state during a later Chandra observation, demonstrating the recurrent nature of CAL 83. Moreover, we found evidence of short-timescale variability in the soft X-ray spectrum. We completed the analysis of the LETG and RGS spectra of CAL 83 with new NLTE line-blanketed model atmospheres that explicitly include 74 ions of the 11 most abundant species. We successfully matched the Chandra and XMM-Newton spectra assuming a model composition with LMC metallicity. We derived the basic stellar parameters of the hot white dwarf, but the current state of atomic data in the soft X-ray domain precludes a detailed chemical analysis. We have obtained the first direct spectroscopic evidence that the white dwarf is massive (Mwd > 1 Msun). The short timescale of the X-ray off-states is consistent with a high white dwarf mass. Our analysis thus provides direct support for supersoft sources as likely progenitors of SN Ia.