  We report the detection of Ly$\alpha$ emission at $\sim9538$\AA{} in the
Keck/DEIMOS and \HST WFC3 G102 grism data from a triply-imaged galaxy at
$z=6.846\pm0.001$ behind galaxy cluster MACS J2129.4$-$0741. Combining the
emission line wavelength with broadband photometry, line ratio upper limits,
and lens modeling, we rule out the scenario that this emission line is \oii at
$z=1.57$. After accounting for magnification, we calculate the weighted average
of the intrinsic Ly$\alpha$ luminosity to be
$\sim1.3\times10^{42}~\mathrm{erg}~\mathrm{s}^{-1}$ and Ly$\alpha$ equivalent
width to be $74\pm15$\AA{}. Its intrinsic UV absolute magnitude at 1600\AA{} is
$-18.6\pm0.2$ mag and stellar mass $(1.5\pm0.3)\times10^{7}~M_{\odot}$, making
it one of the faintest (intrinsic $L_{UV}\sim0.14~L_{UV}^*$) galaxies with
Ly$\alpha$ detection at $z\sim7$ to date. Its stellar mass is in the typical
range for the galaxies thought to dominate the reionization photon budget at
$z\gtrsim7$; the inferred Ly$\alpha$ escape fraction is high ($\gtrsim 10$\%),
which could be common for sub-$L^*$ $z\gtrsim7$ galaxies with Ly$\alpha$
emission. This galaxy offers a glimpse of the galaxy population that is thought
to drive reionization, and it shows that gravitational lensing is an important
avenue to probe the sub-$L^*$ galaxy population.
