The position sensitivity of a thick, cylindrical and continuous 3\u2033 x 3\u2033 (7.62 cm x 7.62 cm) LaBr3:Ce crystal was studied using a 1 mm collimated beam of 662 keV gamma rays from a 400 MBq intense 137Cs source and a spectroscopic photomultiplier (PMT) (HAMAMATSU R6233-100SEL). The PMT entrance window was covered by black absorber except for a small window 1 cm x 1 cm wide. A complete scan of the detector over a 0.5 cm step grid was performed for three positions of the 1 cm x 1 cm window. For each configuration the energy spectrum was measured and the peak centroid, the FWHM, the area and peak asymmetry of the 662 keV gamma transition were analyzed. The data show that, even in a 3\u2033 thick LaBr3:Ce crystal with diffusive surfaces ...