Semi-supervised machine learning (SSL) is gaining popularity as it reduces the cost of training ML models. It does so by using very small amounts of (expensive, well-inspected) labeled data and large amounts of (cheap, non-inspected) unlabeled data. SSL has shown comparable or even superior performances compared to conventional fully-supervised ML techniques. In this paper, we show that the key feature of SSL that it can learn from (non-inspected) unlabeled data exposes SSL to strong poisoning attacks. In fact, we argue that, due to its reliance on non-inspected unlabeled data, poisoning is a much more severe problem in SSL than in conventional fully-supervised ML. Specifically, we design a backdoor poisoning attack on SSL that can be conducted by a weak adversary with no knowledge of target SSL pipeline. This is unlike prior poisoning attacks in fully-supervised settings that assume strong adversaries with practically-unrealistic capabilities. We show that by poisoning only 0.2% of the unlabeled training data, our attack can cause misclassification of more than 80% of test inputs (when they contain the adversary's backdoor trigger). Our attacks remain effective across twenty combinations of benchmark datasets and SSL algorithms, and even circumvent the state-of-the-art defenses against backdoor attacks. Our work raises significant concerns about the practical utility of existing SSL algorithms.