  The far-infrared fine-structure line [CII] at 1900.5\,GHz is known to be one
of the brightest cooling lines in local galaxies, and therefore it has been
suggested to be an efficient tracer for star-formation in very high-redshift
galaxies. However, recent results for galaxies at $z>6$ have yielded numerous
non-detections in star-forming galaxies, except for quasars and submillimeter
galaxies. We report the results of ALMA observations of two lensed,
star-forming galaxies at $z = 6.029$ and $z=6.703$. The galaxy A383-5.1 (star
formation rate [SFR] of 3.2 M$_\odot$ yr$^{-1}$ and magnification of $\mu =
11.4\pm1.9$) shows a line detection with $L_{\rm [CII]} = 8.9\times10^{6}$
L$_\odot$, making it the lowest $L_{\rm [CII]}$ detection at $z>6$. For
MS0451-H (SFR = 0.4 M$_\odot$ yr$^{-1}$ and $\mu = 100\pm20$) we provide an
upper limit of $L_{\rm [CII]} < 3\times10^{5}$ L$_\odot$, which is 1\,dex below
the local SFR-$L_{\rm [CII]}$ relations. The results are consistent with
predictions for low-metallicity galaxies at $z>6$, however, other effects could
also play a role in terms of decreasing $L_{\rm [CII]}$. The detection of
A383-5.1 is encouraging and suggests that detections are possible, but much
fainter than initially predicted.
