In many countries, presidents offer annual addresses to their respective legislatures or citizens. These speeches serve as a platform for leaders to communicate their vision, achievements, and priorities. Presidential speeches are key instruments of political power, serving as tools for agenda-setting and public engagement. However, studies on presidential rhetoric are often limited by traditional methodologies that focus on specific leaders or short periods. This article addresses these limitations by applying Latent Dirichlet Allocation to analyze Chilean presidential speeches from 1832 to 2021, uncovering thematic patterns and their evolution over nearly two centuries. Chile's case, with its stable democratic tradition and rich history of presidential messages, demonstrates Latent Dirichlet Allocation's utility for comprehensive, long-term discourse analysis. Our findings highlight Latent Dirichlet Allocation's effectiveness in capturing thematic shifts that reflect broader socio-political changes, showcasing its potential for studying executive speeches across various political systems. This methodology bridges computational analysis and qualitative inquiry, offering a replicable framework for comparative research. We conclude by discussing its broader implications for future studies on political communication and cross-national analysis.