Using data drawn from the DEEP2 and DEEP3 Galaxy Redshift Surveys, we investigate the relationship between the environment and the structure of galaxies residing on the red sequence at intermediate redshift. Within the massive (10 < log(M*/Msun) < 11) early-type population at 0.4 < z <1.2, we find a significant correlation between local galaxy overdensity (or environment) and galaxy size, such that early-type systems in higher-density regions tend to have larger effective radii (by ~0.5 kpc or 25% larger) than their counterparts of equal stellar mass and Sersic index in lower-density environments. This observed size-density relation is consistent with a model of galaxy formation in which the evolution of early-type systems at z < 2 is accelerated in high-density environments such as groups and clusters and in which dry, minor mergers (versus mechanisms such as quasar feedback) play a central role in the structural evolution of the massive, early-type galaxy population.