An additive Gaussian channel is considered where there are a stochastic signal and a fractional Gaussian noise. The fractional Gaussian noise is the formal derivative of a fractional Brownian motion with the Hurst parameter in the interval (1/2, 1). These processes have a long range dependence and seem to be meaningful models for many physical phenomena. For this communication channel, it is shown that the mutual information between the signal and the channel output can be explicitly expressed as an estimation error. This result generalizes naturally the corresponding result when the noise is white Gaussian.