In many real world graphs, the formation of edges can be influenced by certain sensitive features of the nodes (e.g. their gender, community, or reputation). In this paper we argue that when such influences exist, any downstream Graph Neural Network (GNN) will be implicitly biased by these structural correlations. To allow control over this phenomenon, we introduce the Metadata-Orthogonal Node Embedding Training (MONET) unit, a general neural network architecture component for performing training-time linear debiasing of graph embeddings. MONET operates by ensuring that the node embeddings are trained on a hyperplane orthogonal to that of the node features (metadata). Unlike debiasing approaches in similar domains, our method offers exact guarantees about the correlation between the resulting embeddings and any sensitive metadata. We illustrate the effectiveness of MONET though our experiments on a variety of real world graphs against challenging baselines (e.g. adversarial debiasing), showing superior performance in tasks such as preventing the leakage of political party affiliation in a blog network, and preventing the gaming of embedding-based recommendation systems.