  Faint Lyman-$\alpha$ (Ly$\alpha$) emitters become increasingly rarer towards
the re-ionisation epoch (z~6-7). However, observations from a very large
(~5deg$^2$) Ly$\alpha$ survey at z=6.6 (Matthee et al. 2015) show that this is
not the case for the most luminous emitters. Here we present follow-up
observations of the two most luminous z~6.6 Ly$\alpha$ candidates in the COSMOS
field: `MASOSA' and `CR7'. We used X-SHOOTER, SINFONI and FORS2 (VLT), and
DEIMOS (Keck), to confirm both candidates beyond any doubt. We find redshifts
of z=6.541 and z=6.604 for MASOSA and CR7, respectively. MASOSA has a strong
detection in Ly$\alpha$ with a line width of $386\pm30$ km/s (FWHM) and with
high EW$_0$ (>200 \AA), but it is undetected in the continuum. CR7, with an
observed Ly$\alpha$ luminosity of $10^{43.93\pm0.05}$erg/s is the most luminous
Ly$\alpha$ emitter ever found at z>6. CR7 reveals a narrow Ly$\alpha$ line with
$266\pm15$ km/s FWHM, being detected in the NIR (rest-frame UV, with
$\beta=-2.3\pm0.1$) with an excess in $J$, and also strongly detected in
IRAC/Spitzer. We detect a narrow HeII1640$\AA$ emission line ($6\sigma$) which
explains the excess seen in the $J$ band photometry (EW$_0$~80 \AA). We find no
other emission lines from the UV to the NIR in our X-SHOOTER spectra
(HeII/OIII]1663A>3 and HeII/CIII]1908A>2.5). We find that CR7 is best explained
by a combination of a PopIII-like population which dominates the rest-frame UV
and the nebular emission, and a more normal stellar population which dominates
the mass. HST/WFC3 observations show that the light is indeed spatially
separated between a very blue component, coincident with Ly$\alpha$ and HeII
emission, and two red components (~5 kpc away), which dominate the mass. Our
findings are consistent with theoretical predictions of a PopIII wave, with
PopIII star formation migrating away from the original sites of star formation.
