The age-metallicity relation for F and G dwarf stars in the solar neighborhood, based on the stellar metallicity data of Edvardsson et al. (1993), shows an apparent scatter that is larger than expected considering the uncertainties in metallicities and ages. A number of theoretical models have been put forward to explain the large scatter. However, we present evidence, based on Edvardsson et al. (1993) data, along with Hipparcos parallaxes and new age estimates, that the scatter in the age-metallicity relation depends on the distance to the stars in the sample, such that stars within 30 pc of the Sun show significantly less scatter in [Fe/H]. Stars of intermediate age from the Edvardsson et al. sample at distances 30-80 pc from the Sun are systematically more metal-poor than those more nearby. We also find that the slope of the apparent age-metallicity relation is different for stars within 30 pc than for those stars more distant. These results are most likely an artifact of selection biases in the Edvardsson et al. star sample. We conclude that the intrinsic dispersion in metallicity at fixed age is < 0.15 dex, consistent with the < 0.1 dex scatter for Galactic open star clusters and the interstellar medium.