Frequency modulation of a dilute chromophore’s transition is a common mechanism of line broadening in condensed phases. In many different physical situations this frequency modulation arises from coupling of the chromophore to a collection of flipping two-level systems. In this paper we calculate the absorption line shape for such a chromophore when the two-level systems occupy the sites of a regular lattice. We consider both general and specific (dipolar) two-level system/ chromophore interactions. We present both exact (numerical) and approximate (analytical) expressions for the line shape as a function of the two-level system excitation probability, p, and the flip rate. We find that when p much less than 1 the line shape is Lorentzian for any value of the flip rate,and that when p=1/2 the chromophore’s fluctuating frequency is described approximately by a Gaussian random process, and that therefore the seminal stochastic model of Anderson and Kubo is applicable.