The complex language of eukaryotic gene expression remains incompletely understood. Thus, most of the many noncoding variants statistically associated with human disease have unknown mechanism. Here, we address this challenge using an approach based on a recent machine learning advance—deep convolutional neural networks (CNNs). We introduce an open source package Basset (https://github.com/davek44/Basset) to apply deep CNNs to learn the functional activity of DNA sequences from genomics data. We trained Basset on a compendium of accessible genomic sites mapped in 164 cell types by DNaseI-seq. Basset predictions for the change in accessibility between two variant alleles were far greater for GWAS SNPs that are likely to be causal relative to nearby SNPs in linkage disequilibrium with them. With Basset, a researcher can perform a single sequencing assay in their cell type of interest and simultaneously learn that cell???s chromatin accessibility code and annotate every mutation in the genome with its influence on present accessibility and latent potential for accessibility. Thus, Basset offers a powerful computational approach to annotate and interpret the noncoding genome.