Diagonal interleaving poetry is a new poetic form that generates poems from an initial matrix of words and phrases, using a periodic permutation inspired by interleaving (a technique from error-correcting coding theory). The author introduces this new form in the context of other permutational poetry and wordplay and describes its formal connections with interleaving techniques in coding theory. Poetic and combinatorial constraints and affordances are discussed. Throughout the paper, several n×m matrices of words and phrases are developed as interleaving poems, offering examples of ways that the form can be used to generate interesting poetry.