Recently, Hi-C has been used to probe the 3D chromatin architecture of multiple organisms and cell types. The resulting collections of pairwise contacts across the genome have connected chromatin architecture to many cellular phenomena, including replication timing and gene regulation. However, high resolution (10 kb or finer) contact maps remain scarce due to the expense and time required for collection. A computational method for predicting pairwise contacts without the need to run a Hi-C experiment would be invaluable in understanding the role that 3D chromatin architecture plays in genome biology. We describe Rambutan, a deep convolutional neural network that predicts Hi-C contacts at 1 kb resolution using nucleotide sequence and DNaseI assay signal as inputs. Specifically, Rambutan identifies locus pairs that engage in high confidence contacts according to Fit-Hi-C, a previously described method for assigning statistical confidence estimates to Hi-C contacts. We first demonstrate Rambutan's performance across chromosomes at 1 kb resolution in the GM12878 cell line. Subsequently, we measure Rambutan's performance across six cell types. In this setting, the model achieves an area under the receiver operating characteristic curve between 0.7662 and 0.8246 and an area under the precision-recall curve between 0.3737 and 0.9008. We further demonstrate that the predicted contacts exhibit expected trends relative to histone modification ChIP-seq data, replication timing measurements, and annotations of functional elements such as promoters and enhancers. Finally, we predict Hi-C contacts for 53 human cell types and show that the predictions cluster by cellular function.