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To measure the flux of atmospheric neutrons and study the neutron contribution to the background of the main detector of the PoGOLite (Polarized Gamma-ray Observer) balloon-borne experiment, a thermal-neutron detector with a phoswich system of LiCaAlF6 (Eu) and BGO crystal scintillators is developed. The performance to separate thermal-neutron events from those of gamma-rays and charged particles is validated with 252Cf on ground. The detector is attached to the PoGOLite instrument and is launched in 2011 from the Esrange facility in the North of Sweden. Although the emission wavelength of the LiCaAlF6 (Ce) is ~ 300 nm and overlaps with the absorption wavelength of the BGO, the phoswich capability of the LiCaAlF6 (Ce) with the BGO is also confirmed with installing a waveform shifter.