Dataset distillation methods reduce large-scale datasets to smaller sets of synthetic data, which preserve sufficient information for quickly training a new model from scratch. However, prior work on dataset distillation has focused exclusively on image classification datasets, whereas modern large-scale datasets are primarily in the vision-language space. In this work, we design the first vision-language dataset distillation method, building on the idea of trajectory matching. A key challenge is that vision-language datasets do not have a set of discrete classes. To overcome this, our proposed method jointly distills the image-text pairs in a contrastive formulation. Further, we leverage Low-Rank Adaptation (LoRA) matching to enable more efficient and effective trajectory matching in complex modern vision-language models. Since there are no existing baselines, we compare our distillation approach to three adapted vision-language coreset selection methods. We demonstrate significant improvements on the challenging retrieval benchmarks: for example, on Flickr30K, the best coreset selection method selecting 1000 image-text pairs for training achieves only 5.6% image-to-text retrieval accuracy (i.e., recall@1); in contrast, our dataset distillation approach almost doubles that to 9.9% with just 100 (an order of magnitude fewer) training pairs.