We describe Verse by Verse, our experiment in augmenting the creative process of writing poetry with an AI. We have created a group of AI poets, styled after various American classic poets, that are able to offer as suggestions generated lines of verse while a user is composing a poem. In this paper, we describe the underlying system to offer these suggestions. This includes a generative model, which is tasked with generating a large corpus of lines of verse offline and which are then stored in an index, and a dual-encoder model that is tasked with recommending the next possible set of verses from our index given the previous line of verse.