Natural Language Understanding has witnessed a watershed moment with the introduction of large pre-trained Transformer networks. These models achieve state-of-the-art on various tasks, notably including Natural Language Inference (NLI). Many studies have shown that the large representation space imbibed by the models encodes some syntactic and semantic information. However, to really ``know syntax’’, a model must recognize when its input violates syntactic rules and calculate inferences accordingly. In this work, we find that state-of-the-art NLI models, such as RoBERTa and BART are invariant to, and sometimes even perform better on, examples with randomly reordered words. With iterative search, we are able to construct randomized versions of NLI test sets, which contain permuted hypothesis-premise pairs with the same words as the original, yet are classified with perfect accuracy by large pre-trained models, as well as pre-Transformer state-of-the-art encoders. We find the issue to be language and model invariant, and hence investigate the root cause. To partially alleviate this effect, we propose a simple training methodology. Our findings call into question the idea that our natural language understanding models, and the tasks used for measuring their progress, genuinely require a human-like understanding of syntax.