We report the discovery of a giant Lya emitter (LAE) with a Spitzer/IRAC counterpart near the reionization epoch at z=6.595. The giant LAE is found from the extensive 1 deg^2 Subaru narrow-band survey for z=6.6 LAEs in the Subaru/XMM-Newton Deep Survey (SXDS) field, and subsequently identified by deep spectroscopy of Keck/DEIMOS and Magellan/IMACS. Among our 207 LAE candidates, this LAE is not only the brightest narrow-band object with L(Lya) = 3.9+/-0.2 x 10^43 erg/s in our survey volume of 10^6 Mpc^3, but also a spatially extended Lya nebula with the largest isophotal area whose major axis is at least ~3. This object is more likely to be a large Lya nebula with a size of >~17 kpc than to be a strongly-lensed galaxy by a foreground object. Our Keck spectrum with medium-high spectral and spatial resolutions suggests that the velocity width is v(FWHM)=251+/-21 km/s, and that the line-center velocity changes by ~60 km/s in a 10-kpc range. The stellar mass and star-formation rate are estimated to be 0.9-5.0 x 10^10 Mo and >34 Mo/yr, respectively, from the combination of deep optical to infrared images of Subaru, UKIDSS-Ultra Deep Survey, and Spitzer/IRAC. Although the nature of this object is not yet clearly understood, this could be an important object for studying cooling clouds accreting onto a massive halo, or forming-massive galaxies with significant outflows contributing to cosmic reionization and metal enrichment of inter-galactic medium.
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