  Deep spectroscopic observations of z~6.5 galaxies have revealed a marked
decline with increasing redshift in the detectability of Lyman-alpha emission.
While this may offer valuable insight into the end of the reionisation process,
it presents a fundamental challenge to the detailed spectroscopic study of the
many hundreds of photometrically-selected distant sources now being found via
deep HST imaging, and particularly those bright sources viewed through
foreground lensing clusters. In this paper we demonstrate the validity of a new
way forward via the convincing detection of an alternative diagnostic line,
CIII]1909, seen in spectroscopic exposures of two star forming galaxies at
z=6.029 and 7.213. The former detection is based on a 3.5 hour X-shooter
spectrum of a bright (J=25.2) gravitationally-lensed galaxy behind the cluster
Abell 383. The latter detection is based on a 4.2 hour MOSFIRE spectra of one
of the most distant spectroscopically confirmed galaxies, GN-108036, with
J=25.2. Both targets were chosen for their continuum brightness and
previously-known redshift (based on Lyman-alpha), ensuring that any CIII]
emission would be located in a favorable portion of the near-infrared sky
spectrum. We compare our CIII] and Lyman-alpha equivalent widths in the context
of those found at z~2 from earlier work and discuss the motivation for using
lines other than Lyman-alpha to study galaxies in the reionisation era.
