We introduce the Denoised Web Treebank: a treebank including a normalization layer and a corresponding evaluation metric for dependency parsing of noisy text, such as Tweets. This benchmark enables the evaluation of parser robustness as well as text normalization methods, including normalization as machine translation and unsupervised lexical normalization, directly on syntactic trees. Experiments show that text normalization together with a combination of domain-specific and generic part-of-speech taggers can lead to a significant improvement in parsing accuracy on this test set