We show that local fields can increase the rotatory power r of nonconductors by a factor of 10-in contrast to the typical 10% effect in other properties. We present calculations for quartz and Se, and a general method to estimate the size of local-field corrections. Notably, only scalar local fields are needed despite the vector character of light. A self-energy-corrected local-density band structure yields corrections to r of a factor of 17 in quartz and 24 in Se. These values are 30% above experiment for quartz, and, for one sign choice, within the 50% error bars for Se.