Climate records from over much of the world show variability on both Milankovitch and millennial timescales. However, mechanisms in the climate system that have a global scale are lacking. In this two-part paper, we turn attention to a part of the system that is known from the modern climate record to be capable of organizing global scale climate events: the tropics. In the first part, we isolate this system using a coupled ocean-atmosphere model of the tropical Pacific. The model results demonstrate a tropical mechanism which can amplify Milankovitch forcing and generate a mean climate response. The model is also run for 150,000 years with no forcing. The results raise the possibility that millennial timescale variability can be generated within the tropics through non-linear interactions. In that case, power is to be expected over a range of frequencies, rather than in any particular narrow band. The second part of our study, presented in the following paper, will discuss the potential impact on the global climate of these mechanisms of tropical climate variability.