To further our understanding of immunopeptidomics, improved tools are needed to identify peptides presented by major histocompatibility complex class I (MHC-I). Many existing tools are limited by their reliance upon chemical affinity data, which is less biologically relevant than sampling by mass spectrometry, and other tools are limited by incomplete exploration of machine learning approaches. Herein, we assemble publicly available data describing human peptides discovered by sampling the MHC-I immunopeptidome with mass spectrometry and use this database to train random forest classifiers (ForestMHC) to predict presentation by MHC-I. As measured by precision in the top 1% of predictions, our method outperforms NetMHC and NetMHCpan on test sets, and it outperforms both these methods and MixMHCpred on new data from an ovarian carcinoma cell line. We also find that random forest scores correlate monotonically, but not linearly, with known chemical binding affinities, and an information-based analysis of classifier features shows the importance of anchor positions for our classification. The random-forest approach also outperforms a deep neural network and a convolutional neural network trained on identical data. Finally, we use our large database to confirm that gene expression partially determines peptide presentation. ForestMHC is a promising method to identify peptides bound by MHC-I. We have demonstrated the utility of random forest-based approaches in predicting peptide presentation by MHC-I, assembled the largest known database of MS binding data, and mined this database to show the effect of gene expression on peptide presentation. ForestMHC has potential applicability to basic immunology, rational vaccine design, and neoantigen binding prediction for cancer immunotherapy. This method is publicly available for applications and further validation.