Compliance is the act or status of complying with an imperative regulatory or normative requirement, that is, compliance means working within boundaries defined by contractual, social, or cultural standards. The aim of this narrative review is to use the food supply chain as a lens of enquiry to distinguish between compliance-based and integrity-based organizational climates and frame and rationalize why deviant behavior arises and how it can be identified. Contemporary theory is explored and critiqued using case studies to contextualize the challenge of organizations promoting supply chain compliance and at the same time recognizing the need for deviant behavior to occur in order to drive innovation and continuous improvement within food supply chains. Deviant behavior can be perceived as either positive in terms of driving continuous improvement or destructive where this behavior has a negative impact on the organization. Although multiple cultural maturity models seek to characterize positive food safety culture and climate, there is minimal research that focuses on the characterization of deviant negative behavior or the development of early warning systems designed to pinpoint signals, traits, or characteristics of this behavior such as low staff morale, theft, property destruction, or absenteeism. The use of cultural maturity models and assessment tools is of value in assisting organizations to translate from a rule, instrumental, or compliance-based organizational climate to an ethically strong organizational climate that focuses on integrity, building trust, and values and a new cultural maturity model is proposed and explored.