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.