Are there a set of basic operations that are used as building blocks of computation in the brain? If so, what are these operations? An ideal paradigm for studying this question is 2D path integration: the task of keeping track of one's spatial position over time through incremental addition of displacement vectors. Path integration is a compelling computation to study in that there are many constraints in how one can break it down into simpler operations. Moreover, small-brained organisms like bees, ants, and fruit flies with tractable nervous systems seem able to implement this computation (Heinze et al. 2018, Kim & Dickinson 2017). A major impediment to the study of insect path integration has been the absence of a head-fixed behavioral setup in a model organism like Drosophila melanogaster where the memory of a spatial location can be learned and reliably reported by the animal. As a step in this direction, we developed a new virtual reality preparation that constrains the head-fixed fruit flies to walk along circular or linear paths. We show that the flies' internal compass accurately reflects the fly's virtual orientation in this preparation. Furthermore, we have preliminary evidence of flies using spatial memory in this setup.