Let K be an arbitrary Kripke model of Heyting Arithmetic, HA. For every node k in K, we can view the classical structure of k, m_k, as a model of some classical theory of arithmetic. Let T be a classical theory in the language of arithmetic. We say K is locally T, iff for every k in K, m_k models T. A well-studied question in the model theory of HA is the following question: Is every Kripke model of HA locally PA? We answer this question negatively by constructing a Kripke model of HA which is not locally B\Sigma_1.