Deep spectroscopic observations of z 6.5 galaxies have revealed a marked decline with increasing redshift in the detectability of Ly α emission. While this may offer valuable insight into the end of the reionization process, it presents a challenge to the detailed spectroscopic study of bright photometrically-selected distant sources now being found via deep Hubble Space Telescope imaging, and particularly those highly magnified sources viewed through foreground lensing clusters. In this paper, we demonstrate the validity of a new way forward via the detection of an alternative diagnostic line, C III] λ1909 Å, seen in spectroscopic exposures of a star-forming galaxy at z Lyα = 6.029. We also report tentative detection of C III] λ1909 Å in a galaxy at z Lyα = 7.213. The former 3.3σ detection is based on a 3.5 h XShooter spectrum of a bright (J 125 = 25.2) gravitationally-lensed galaxy behind the cluster Abell 383. The latter 2.8σ detection is based on a 4.2 h MOSFIRE spectra of one of the most distant spectroscopically confirmed galaxies, GN-108036, with J 140 = 25.2. Both targets were chosen for their continuum brightness and previously-known redshift (based on Ly α), ensuring that any C III] emission would be located in a favourable portion of the near-infrared sky spectrum. Since the availability of secure Ly α redshifts significantly narrows the wavelength range where C III] is sought, this increases confidence in these, otherwise, low-signal-to-noise ratio detections. We compare our C III] and Ly α equivalent widths in the context of those found at z 2 from earlier work and discuss the motivation for using lines other than Ly α to study galaxies in the reionization era.