Literary translation is a culturally significant task, but it is bottlenecked by the small number of qualified literary translators relative to the many untranslated works published around the world. Machine translation (MT) holds potential to complement the work of human translators by improving both training procedures and their overall efficiency. Literary translation is less constrained than more traditional MT settings since translators must balance meaning equivalence, readability, and critical interpretability in the target language. This property, along with the complex discourse-level context present in literary texts, also makes literary MT more challenging to computationally model and evaluate. To explore this task, we collect a dataset (Par3) of non-English language novels in the public domain, each aligned at the paragraph level to both human and automatic English translations. Using Par3, we discover that expert literary translators prefer reference human translations over machine-translated paragraphs at a rate of 84%, while state-of-the-art automatic MT metrics do not correlate with those preferences. The experts note that MT outputs contain not only mistranslations, but also discourse-disrupting errors and stylistic inconsistencies. To address these problems, we train a post-editing model whose output is preferred over normal MT output at a rate of 69% by experts. We publicly release Par3 to spur future research into literary MT.