Chikungunya is an arthropod-borne disease caused by the Asian tiger mosquito, Aedes albopictus. It can be an important burden to public health and a great cause of morbidity and, sometimes, mortality. Understanding if and when disease control measures should be taken is key to curtail its spread. Dumont and Chiroleu (Math Biosc Eng 7(2):315–348, 2010) showed that the use of chemical control tools such as adulticide and larvicide, and mechanical control, which consists of reducing the breeding sites, would have been useful to control the explosive 2006 epidemic in Réunion Island. Despite this, chemical control tools cannot be of long-time use, because they can induce mosquito resistance, and are detrimental to the biodiversity. It is therefore necessary to develop and test new control tools that are more sustainable, with the same efficacy (if possible). Mathematical models of sterile insect technique (SIT) to prevent, reduce, eliminate or stop an epidemic of Chikungunya are formulated and analysed. In particular, we propose a new model that considers pulsed periodic releases, which leads to a hybrid dynamical system. This pulsed SIT model is coupled with the human population at different epidemiological states in order to assess its efficacy. Numerical simulations for the pulsed SIT, using an appropriate numerical scheme are provided. Analytical and numerical results indicate that pulsed SIT with small and frequent releases can be an alternative to chemical control tools, but only if it is used or applied early after the beginning of the epidemic or as a preventive tool