Text-conditional medical image generation is vital for radiology, augmenting small datasets, preserving data privacy, and enabling patient-specific modeling. However, its applications in 3D medical imaging, such as CT and MRI, which are crucial for critical care, remain unexplored. In this paper, we introduce GenerateCT, the first approach to generating 3D medical imaging conditioned on free-form medical text prompts. GenerateCT incorporates a text encoder and three key components: a novel causal vision transformer for encoding 3D CT volumes, a text-image transformer for aligning CT and text tokens, and a text-conditional super-resolution diffusion model. Without directly comparable methods in 3D medical imaging, we benchmarked GenerateCT against cutting-edge methods, demonstrating its superiority across all key metrics. Importantly, we explored GenerateCT's clinical applications by evaluating its utility in a multi-abnormality classification task. First, we established a baseline by training a multi-abnormality classifier on our real dataset. To further assess the model's generalization to external datasets and its performance with unseen prompts in a zero-shot scenario, we employed an external dataset to train the classifier, setting an additional benchmark. We conducted two experiments in which we doubled the training datasets by synthesizing an equal number of volumes for each set using GenerateCT. The first experiment demonstrated an 11% improvement in the AP score when training the classifier jointly on real and generated volumes. The second experiment showed a 7% improvement when training on both real and generated volumes based on unseen prompts. Moreover, GenerateCT enables the scaling of synthetic training datasets to arbitrary sizes. As an example, we generated 100,000 3D CT volumes, fivefold the number in our real dataset, and trained the classifier exclusively on these synthetic volumes. Impressively, this classifier surpassed the performance of the one trained on all available real data by a margin of 8%. Lastly, domain experts evaluated the generated volumes, confirming a high degree of alignment with the text prompts. Access our code, model weights, training data, and generated data at https://github.com/ibrahimethemhamamci/GenerateCT