We use first-principles density functional theory calculations to investigate the dielectric response of BaZrO3 perovskite. A previous study reported a disagreement between experimental and theoretical low temperature dielectric constant for the high symmetry BaZrO3 structure. We show that a fully relaxed 40 atom BaZrO3 structure exhibits O6 octahedral tilting, and that agrees with experiment. The change in from high-symmetry to low-symmetry structure is due to increased phonon frequencies as well as decreased mode effective charges.