This Letter reports on the fabrication of long period fiber gratings having subnanometric bandwidths in the 1500 nm spectral region. Large gratings have been photo inscribed in a high NA fiber; the grating pitch and the order of the HE cladding mode are optimized to produce gratings with a large number of periods and prevent the coupling to TE, TM, or EH modes. Resonances with a FWHM of 0.83 and 0.68 nm have been achieved for gratings 15 and 20 cm long, respectively; the free spectral range between the transmission notches is 125 nm. The polarization effects and the sensitivity of the gratings to temperature and to strain variations are presented as well.