Large languages models (LLMs) trained on datasets of publicly available source code have established a new state-of-the-art in code completion. However, these models are mostly unaware of the code that already exists within a specific project, preventing the models from making good use of existing APIs. Instead, LLMs often invent, or "hallucinate", non-existent APIs or produce variants of already existing code. Although the API information is available to IDEs, the input size limit of LLMs prevents code completion techniques from including all relevant context into the prompt. This paper presents De-Hallucinator, an LLM-based code completion technique that grounds the predictions of a model through a novel combination of retrieving suitable API references and iteratively querying the model with increasingly suitable context information in the prompt. The approach exploits the observation that LLMs often predict code that resembles the desired completion, but that fails to correctly refer to already existing APIs. De-Hallucinator automatically identifies project-specific API references related to the code prefix and to the model's initial predictions and adds these references into the prompt. Our evaluation applies the approach to the task of predicting API usages in open-source Python projects. We show that De-Hallucinator consistently improves the predicted code across four state-of-the-art LLMs compared to querying the model only with the code before the cursor. In particular, the approach improves the edit distance of the predicted code by 23-51% and the recall of correctly predicted API usages by 24-61% relative to the baseline.

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