Contrastive vision-language representation learning has achieved state-of-the-art performance for zero-shot classification, by learning from millions of image-caption pairs crawled from the internet. However, the massive data that powers large multimodal models such as CLIP, makes them extremely vulnerable to various types of targeted data poisoning and backdoor attacks. Despite this vulnerability, robust contrastive vision-language pre-training against such attacks has remained unaddressed. In this work, we propose ROCLIP, the first effective method for robust pre-training multimodal vision-language models against targeted data poisoning and backdoor attacks. ROCLIP effectively breaks the association between poisoned image-caption pairs by considering a relatively large and varying pool of random captions, and matching every image with the text that is most similar to it in the pool instead of its own caption, every few epochs.It also leverages image and text augmentations to further strengthen the defense and improve the performance of the model. Our extensive experiments show that ROCLIP renders state-of-the-art targeted data poisoning and backdoor attacks ineffective during pre-training CLIP models. In particular, ROCLIP decreases the success rate for targeted data poisoning attacks from 93.75% to 12.5% and that of backdoor attacks down to 0%, while improving the model's linear probe performance by 10% and maintains a similar zero shot performance compared to CLIP. By increasing the frequency of matching, ROCLIP is able to defend strong attacks, which add up to 1% poisoned examples to the data, and successfully maintain a low attack success rate of 12.5%, while trading off the performance on some tasks.