Many biological processes are governed by protein-ligand interactions. Of such is the recognition of self and nonself cells by the immune system. This immune response process is regulated by the major histocompatibility complex (MHC) protein which is encoded by the human leukocyte antigen (HLA) complex. Understanding the binding potential between MHC and peptides is crucial to our understanding of the functioning of the immune system, which in turns will broaden our understanding of autoimmune diseases and vaccine design. We introduce a new distributed representation of amino acids, named HLA-Vec, that can be used for a variety of downstream proteomic machine learning tasks. We then propose a deep convolutional neural network architecture, named HLA-CNN, for the task of HLA class I-peptide binding prediction. Experimental results show combining the new distributed representation with our HLA-CNN architecture achieves state-of-the-art results in the vast majority of the latest two Immune Epitope Database (IEDB) weekly automated benchmark datasets.