Oil production must decline substantially over the coming decades to stay within climate-safe limits. Current oil company business models are not prepared for the production decline required by climate-safe pathways. The two opposing facts create a dissonance and inhibit oil company business strategy from entering the opportunity space. The opportunity space is where the possible becomes the profitable within the constraints of what is feasible and socially acceptable. Transition Engineering is a transdisciplinary engineering approach that applies systems thinking, risk management, and systems engineering to resolve wicked problems of the energy transition. This article applies Transition Engineering to the wicked problem of the future business of oil companies. A workshop series was conducted with oil industry experts from various backgrounds. The result was the realisation of an opportunity space which dispelled the dissonance surrounding the wicked problem. Transition Engineering tools shifted participants’ focus from the dissonance surrounding the wicked problem to the exploration of the opportunity space. Another result is contributions to the use of Transition Engineering tools in complex upstream energy industry scenarios. Future work will enter the opportunity space and design business model options and strategies.