Chagaś disease is a human health problem in Latin America. It is highly prevalent in northern Chile between the Arica-Parinacota and Coquimbo regions, with reported incidence of 3-11/100000 inhabitants and mortality of 0.3-0.4/100000. The interruption of vector transmission was reported in 1999 by means of the elimination of the primary vector, Triatoma infestans, from human dwellings, thus the epidemiologic dynamics of this disease should be modified. Here we model the dynamics of Chagaś disease based on previous models for vector and congenital transmission, propose a model that includes both transmission forms and perform simulations. We derive useful relationships for the reproductive number (R0) showing that it may be expressed as the sum of the vector (R0V) and congenital (R0C) contributions. The vector contribution is larger than the congenital one; without the former Chagaś disease vanishes exponentially in two to three generations. Sensitivity analyses showed that the main parameters that intervene are the human bite rate, the density of vectors per human and the mortality rate of the insect vectors. Our model showed that the success of the eradication of Chagaś disease is based on the interruption of domestic transmission. Once this is obtained, the control strategies should focus on avoiding the domiciliation of wild vectors, re-colonization by the primary vector, and an adequate coverage of congenital case treatment.