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, nor any signatures of Wolf-Rayet (WR) stars. 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.