We report measurements of dielectric permittivity and dielectric losses at microwave frequencies of Lanthanum Gallium Silicate as a function of temperature. The dielectric rod resonator method was used to evaluate the two relative permittivity tensor components eps t and eps z of this uniaxial dielectric crystal. Between 10 and 400 K, eps t varies from 18.92 to 19.65 whereas eps z ranges from 60.81 to 46.66. Around 300 K, the temperature coefficients of eps t and eps z have opposite signs and are equal to 130 and -720 ppm/K, respectively. This characteristic enables one to design a self-compensated microwave resonator presenting a low frequency temperature sensitivity. For the measured dielectric sample the dielectric losses range from 10-4 to 5.10-6 between 300 and 20 K and are actually limited by the crystal quality