  We report the spectroscopic confirmation of two Lyman break galaxies at
redshift > 7. The galaxies were observed as part of an ultra-deep spectroscopic
campaign with FORS2 at the ESO/VLT for the confirmation of z~7 ``z--band
dropout'' candidates selected from our VLT/Hawk-I imaging survey. Both galaxies
show a prominent emission line at 9735A and 9858A respectively: the lines have
fluxes of ~ 1.6-1.2 x 10^(-17) erg/s/cm2 and exhibit a sharp decline on the
blue side and a tail on the red side. The asymmetry is quantitatively
comparable to the observed asymmetry in z ~ 6 Ly-alpha lines, where absorption
by neutral hydrogen in the IGM truncates the blue side of the emission line
profile. We carefully evaluate the possibility that the galaxies are instead at
lower redshift and we are observing either [OII], [OIII] or H-alpha emission:
however from the spectroscopic and the photometric data we conclude that there
are no other plausible identifications, except for Ly-alpha at redshift >7,
implying that these are two of the most robust redshift determination for
galaxies in the reionization epoch. Based on their redshifts and broad--band
photometry, we derive limits on the star formation rate and on the ultraviolet
spectral slopes of the two galaxies. We argue that these two galaxies alone are
unlikely to have ionized the IGM in their surroundings.
