We tackle the challenge of topic classification of tweets in the context of analyzing a large collection of curated streams by news outlets and other organizations to deliver relevant content to users. Our approach is novel in applying distant supervision based on semi-automatically identifying curated streams that are topically focused (for example, on politics, entertainment, or sports). These streams provide a source of labeled data to train topic classifiers that can then be applied to categorize tweets from more topically-diffuse streams. Experiments on both noisy labels and human ground-truth judgments demonstrate that our approach yields good topic classifiers essentially "for free", and that topic classifiers trained in this manner are able to dynamically adjust for topic drift as news on Twitter evolves.