We report muon spin relaxation and {69,71}Ga nuclear quadrupolar resonance local-probe investigations of the kagome compound Pr3Ga5SiO14. Small quasistatic random internal fields develop below 40 K and persist down to our base temperature of 21 mK. They originate from hyperfine-enhanced 141Pr nuclear magnetism which requires a nonmagnetic Pr3+ crystal-field (CF) ground state. In addition, we observe a broad maximum of the relaxation rate at approximately 10 K which we attribute to the population of the first excited magnetic CF level. Our results yield a Van Vleck paramagnet picture, at variance with the formerly proposed spin-liquid ground state.