The packaging of DNA inside a nucleus shows complex structure stabilized by a host of DNA-bound factors. Both the distribution of these factors and the contacts between different genomic locations of the DNA can now be measured on a genome-wide scale. This has advanced the development of models aimed at predicting the conformation of DNA given only the locations of bound factors-the chromatin folding problem. Here we present a maximum-entropy model that is able to predict a contact map representation of structure given a sequence of bound factors. Non-local effects due to the sequence neighborhood around contacting sites are found to be important for making accurate predictions. Lastly, we show that the model can be used to infer a sequence of bound factors given only a measurement of structure. This opens up the possibility for efficiently predicting sequence regions that may play a role in generating cell-type specific structural differences.