Phosphorylation of histone H3 threonine 3 (H3T3) by Haspin recruits the chromosomal passenger complex to the inner centromere and ensures proper cell cycle progression through mitosis. The mechanism by which Haspin binds to nucleosomes to phosphorylate H3T3 is not known. We report here cryo-EM structures of the Haspin kinase domain bound to a nucleosome. In contrast with previous structures of histone-modifying enzymes, Haspin solely contacts the nucleosomal DNA, inserting into a supergroove formed by apposing major grooves of two DNA gyres. This unique binding mode provides a plausible mechanism by which Haspin can bind to nucleosomes in a condensed chromatin environment to phosphorylate H3T3. We identify key basic residues in the Haspin kinase domain that are essential for phosphorylation of nucleosomal histone H3 and binding to mitotic chromatin. Our structure is the first of a kinase domain bound to a nucleosome and is the first example of a histone-modifying enzyme that binds to nucleosomes solely through DNA contacts.