  We consider the stochastic model for the propagation of a rumour within a
population which was formulated by Maki and Thompson. Sudbury established that,
as the population size tends to infinity, the proportion of the population
never hearing the rumour converges in probability to $0.2032$. Watson later
derived the asymptotic normality of a suitably scaled version of this
proportion. We prove a corresponding large deviations principle, with an
explicit formula for the rate function.
