Accurate ($\lesssim 1\% $) predictions for the anisotropy of the Cosmic Background Radiation (CBR) are essential for using future high-resolution ($\lesssim 1^\circ$) CBR maps to test cosmological models. In many inflationary models the variation (``running'') of the spectral index of the spectrum of density perturbations is a significant effect and leads to changes of around 1\% to 10\% in the CBR power spectrum. We propose a general method for taking running into account which uses the derivative of the spectral index ($dn/d\ln k$). Conversely, high-resolution CBR maps may be able to determine $dn/d\ln k$, giving important information about the inflationary potential.

Discussion of calculation clarified; error corrected which reduces estimated effect for chaotic inflation