The prevention of tropical forest deforestation is essential for mitigating climate change. We tested the machine learning algorithm Maxent to predict deforestation across the Peruvian Amazon. We used official annual 2001-2019 deforestation data to develop a predictive model and to test the model's accuracy using near-real-time forest loss data for 2020. Distance from agricultural land and distance from roads were the predictor variables that contributed most to the final model, indicating that a narrower set of variables contribute nearly 80% of the information necessary for prediction at scale. The permutation importance indicating variable information not present in the other variables was also highest for distance from agricultural land and distance from roads, at 40.5% and 14.3%, respectively. The predictive model registered 73.2% of the 2020 early alerts in a high or very high risk category; less than 1% of forest cover in national protected areas were registered as very high risk, but buffer zones were far more vulnerable, with 15% of forest cover being in this category. To our knowledge, this is the first study to use 19 years of annual data for deforestation risk. The open-source machine learning method could be applied to other forest regions, at scale, to improve strategies for reducing future deforestation.