Photoluminescence (PL) from purified (>90%) double-wall carbon nanotubes (DWNTs), which have beensynthesized by zeolite catalyst-supported chemical vapor deposition (zeolite-CCVD), of very small diameters(0.8-nm average inner tube) is reported. The PL contour mappings for various ratios (1-90%) of double-versus single-wall carbon nanotubes by thermal oxidation have enabled us to unambiguously identify thechirality of inner tubes for the DWNTs synthesized. After the extensive high-temperature oxidation at 700
C, high-purity (>90%) DWNTs of ~0.8 nm inner diameter are obtained, and most of these correspond tothe DWNTs having inner tubes with chiralities of (7,5), (7,6), and (9,4).