Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)We consider the stochastic model for the propagation of a rumour within a population which was formulated by Maki and Thompson [20]. Sudbury [22] 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 [23] 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. (C) 2015 Elsevier Inc. All rights reserved.4321 142155Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)PRP-FAEPEX-UNICAMP [016/2013]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CNPq [303872/2012-8]