Optical conductivity measurements on the perovskite-related oxide CaCu3Ti4O12 provide a hint of the physics underlying the observed giant dielectric effect in this material. A low-frequency vibration displays anomalous behavior, implying that there is a redistribution of charge within the unit cell at low temperature. At infrared frequencies (terahertz), the value for the dielectric constant is approximately 80 at room temperature, which is far smaller than the value of approximately 10(5) obtained at lower radio frequencies (kilohertz). This discrepancy implies the presence of a strong absorption at very low frequencies due to dipole relaxation. At room temperature, the characteristic relaxation times are fast (less than or approximately 500 nanoseconds) but increase dramatically at low temperature, suggesting that the large change in dielectric constant may be due to a relaxor-like dynamical slowing down of dipolar fluctuations in nanosize domains.