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We present the spectroscopic confirmation of the brightest known gravitationally lensed Lyman-break galaxy in the Epoch of Reionization (EoR), A1703-zD1, through the detection of [C ii] 158 $\mu$m at a redshift of z = 6.8269 ± 0.0004. This source was selected behind the strong lensing cluster Abell 1703, with an intrinsic luminosity and a very blue Spitzer/Infrared Array Camera (IRAC) [3.6]–[4.5] colour, implying high equivalent width line emission of [O iii] + Hβ. [C ii] is reliably detected at 6.1σ cospatial with the rest-frame ultraviolet (UV) counterpart, showing similar spatial extent. Correcting for the lensing magnification, the [C ii] luminosity in A1703-zD1 is broadly consistent with the local $L_{\rm [C\, {\small II}]}$–star formation rate (SFR) relation. We find a clear velocity gradient of 103 ± 22 km $\rm s^{-1}$ across the source that possibly indicates rotation or an ongoing merger. We furthermore present spectral scans with no detected [C ii] above 4.6σ in two unlensed Lyman-break galaxies in the Extended Groth Strip (EGS)-Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) field at z ∼ 6.6–6.9. This is the first time that the Northern Extended Millimeter Array (NOEMA) has been successfully used to observe [C ii] in a ‘normal’ star-forming galaxy at z > 6, and our results demonstrate its capability to complement the Atacama Large Millimeter/submillimeter Array (ALMA) in confirming galaxies in the EoR.