Publicly Verifiable Outsourced Computation (PVC) allows devices with restricted resources to delegate expensive computations to more powerful external servers, and to verify the correctness of results. Whilst highlybeneficial in many situations, this increases the visibility and availability of potentially sensitive data, so we may wish to limit the sets of entities that can view input data and results. Additionally, it is highly unlikely that all users have identical and uncontrolled access to all functionality within an organization. Thus there is a need for access control mechanisms in PVC environments.In this work, we define a new framework for Publicly Verifiable Outsourced Computation with Access Control (PVC-AC). We formally define algorithms to provide different PVC functionality for each entity within a large outsourced computation environment, and discuss the forms of access control policies that are applicable, and necessary, in such environments, as well as formally modelling the resulting security properties. Finally, we give an example instantiation that (in a black-box and generic fashion) combines existing PVC schemes with symmetric Key Assignment Schemes to cryptographically enforce the policies of interest.