We report an optical detection of an extended structure around a QSO at z=6.43 (CFHQSJ2329-0301, the highest redshift QSO currently known) in deep z and z_r-band images of the Subaru/Suprime-Cam. After a careful PSF (QSO) subtraction, a structure in the z-band extends more than 4 on the sky (R_e=11 kpc), and thus, is well-resolved (16sigma detection). The PSF-subtracted z_r-band structure is in a similar shape to that in the z-band, but less significant with a 3 sigma detection. In the z-band, a radial profile of the QSO+host shows a clear excess over that of the averaged PSF in 0.8-3 radius. Since the z-band includes a Lya emission at z=6.43, the z flux is perhaps a mixture of the host (continuum light) and its Lya emission, whereas the z_r-band flux is from the host. Through a SED modeling, we estimate 40% of the PSF-subtracted z-band light is from the host (continuum) and 60% is from Lya emission. The absolute magnitude of the host is M_{1450}=-23.9 (c.f. M_{1450}=-26.4 for the QSO). A lower limit of the SFR(Lya) is 1.6 Msun yr^{-1} with stellar mass ranging 6.2 x 10^8 to 1.1 x 10^10 Msun when 100 Myrs of age is assumed. The detection shows that a luminous QSO is already harbored by a large, star-forming galaxy in the early Universe only after ~840 Myr after the big bang. The host may be a forming giant galaxy, co-evolving with a super massive black hole.
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