We have performed deep imaging surveys for LyA emitters (LAEs) at redshift ~7.3 in two blank fields, the Subaru Deep Field (SDF) and the Subaru/XMM-Newton Deep survey Field (SXDF), using the Subaru/Suprime-Cam equipped with new red-sensitive CCDs and a new narrow-band filter, NB1006 (lambda_c=10052 Ang, FWHM=214 Ang). We identified four objects as LAE candidates that exhibit luminosity excess in NB1006. By carrying out deep follow-up spectroscopy for three of them using Subaru/FOCAS and Keck/DEIMOS, a definitively asymmetric emission line is detected for one of them, SXDF-NB1006-2. Assuming this line is LyA, this object is a LAE at z=7.215 which has luminosity of 1.2^{+1.5}_{-0.6} x 10^43 [erg s-1] and a weighted skewness S_w=4.90+-0.86. Another object, SDF-NB1006-2, shows variable photometry and is thus probably a quasar (QSO) or an active galactic nucleus (AGN). It shows an asymmetric emission line at 10076 Ang, which may be due to either LyA at z=7.288 or [OII] at z=1.703. The third object, SDF-NB1006-1, is likely a galaxy with temporal luminosity enhancement associated with a supernova explosion, as the brightness of this object varies between the observed epochs. Its spectrum does not show any emission lines. The inferred decrease in the number density of LAEs toward higher redshift is n_LyA(z=7.3)/n_LyA(z=5.7) = 0.05^+0.11_-0.05 from z=5.7 to 7.3 down to L(LyA)=1.0 x 10^43 [erg s-1]. The present result is consistent with the interpretation in previous studies that the neutral hydrogen fraction is rapidly increasing from z=5.7 to 7.3.
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