We consider the spectral diffusion:of a chromophore coupled through dipolar interactions to a regular lattice of flipping two-level systems. In particular, we calculate the spectral diffusion kernel, P(omega,t/omega(0)), which is the conditional probability density that the chromophore will have transition frequency omega at time t, given that it had frequency omega(0) at time 0. At very short times we find that the spectral diffusion kernel is Lorentzian, for any value of the two-level system excitation probability, p. For longer times the form of the spectral diffusion kernel depends on the value of p. We derive several approximate expressions for the spectral diffusion kernel, all of which go to the correct equilibrium distribution of frequencies for long times. For p similar or equal to 1/2, when the frequency distribution; is nearly Gaussian, we find that the spectral diffusion kernel is not at all Gaussian for short times. We compare all of our approximate expressions with numerically exact results. Motivated by certain optical spectral diffusion experiments on individual molecules in solids, we also calculate P(Delta;T), the distribution of spectral jumps, which is the probability density that the chromophore’s frequency will change by an amount Delta in time t. In a subsequent paper we will analyze these spectral-diffusion experiments with our results.