We report highly birefringent fiber Bragg gratings in standard single-mode optical fiber realized with UV femtosecond pulses and line-by-line inscription. By controlling the three-dimensional positioning of the focused laser beam with respect to the fiber core, we achieve very high birefringence at the grating location in a single exposure. A maximum birefringence value of 7.93×10(-4) has been reached for 10th-order gratings when using 2 μJ pulses, which is to our knowledge the highest birefringence value reported so far. This birefringence results from UV-induced high-densification lines shifted from the center of the core, increasing the asymmetry of the induced-stress lines. With a Bragg wavelength spacing reaching more than 800 pm between polarization modes, such gratings are particularly well suited for selective filtering or, as demonstrated here, for temperature-insensitive transverse-strain measurements.