  Twenty-one centimeter tomography is emerging as a powerful tool to explore
the end of the cosmic dark ages and the reionization epoch, but it will only be
as good as our ability to accurately model and remove astrophysical foreground
contamination. Previous treatments of this problem have focused on the angular
structure of the signal and foregrounds and what can be achieved with limited
spectral resolution (bandwidths in the 1 MHz range). In this paper we introduce
and evaluate a ``blind'' method to extract the multifrequency 21cm signal by
taking advantage of the smooth frequency structure of the Galactic and
extragalactic foregrounds. We find that 21 cm tomography is typically limited
by foregrounds on scales $k\ll 1h/$Mpc and limited by noise on scales $k\gg
1h/$Mpc, provided that the experimental bandwidth can be made substantially
smaller than 0.1 MHz. Our results show that this approach is quite promising
even for scenarios with rather extreme contamination from point sources and
diffuse Galactic emission, which bodes well for upcoming experiments such as
LOFAR, MWA, PAST, and SKA.
