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In this paper, the numerical and the experimental analyses of coated long-period fiber gratings (LPFGs) as a high-sensitivity optochemical sensor are presented. The proposed structure relies on LPFGs coated with nanoscale high refractive index chemical-sensitive overlays. The deposition of overlays with refractive index higher than the cladding one leads to a modification of the cladding-mode distribution. If the overlay features are properly chosen, a strong field enhancement within the overlay occurs, leading to an excellent sensitivity of the cladding-mode distribution to the coating properties. The effects of overlay thickness and cladding-mode order on sensor performances have been numerically and experimentally investigated. In order to provide a high-sensitivity and species-specific optochemical sensor, this mechanism has been proved with nanoscale overlays of syndiotactic polystyrene (sPS) in the nanoporous crystalline δ form. The sensitive material has been chosen in light of its selectivity and high sorption properties towards chlorinated and aromatic compounds. Sensor probes were prepared by using dip-coating technique and an adequate procedure to obtain the δ-form sPS. Experimental demonstration of the sensor capability to perform subparts-per-million detection of chloroform in water at room temperature is also reported.