We address the task of Named Entity Disambiguation (NED) for noisy text. We present WikilinksNED, a large-scale NED dataset of text fragments from the web, which is significantly noisier and more challenging than existing news-based datasets. To capture the limited and noisy local context surrounding each mention, we design a neural model and train it with a novel method for sampling informative negative examples. We also describe a new way of initializing word and entity embeddings that significantly improves performance. Our model significantly outperforms existing state-of-the-art methods on WikilinksNED while achieving comparable performance on a smaller newswire dataset.