Deepfake attacks, malicious manipulation of media containing people, are a serious concern for society. Conventional deepfake detection methods train supervised classifiers to distinguish real media from previously encountered deepfakes. Such techniques can only detect deepfakes similar to those previously seen, but not zero-day (previously unseen) attack types. As current deepfake generation techniques are changing at a breathtaking pace, new attack types are proposed frequently, making this a major issue. Our main observations are that: i) in many effective deepfake attacks, the fake media must be accompanied by false facts i.e. claims about the identity, speech, motion, or appearance of the person. For instance, when impersonating Obama, the attacker explicitly or implicitly claims that the fake media show Obama; ii) current generative techniques cannot perfectly synthesize the false facts claimed by the attacker. We therefore introduce the concept of "fact checking", adapted from fake news detection, for detecting zero-day deepfake attacks. Fact checking verifies that the claimed facts (e.g. identity is Obama), agree with the observed media (e.g. is the face really Obama's?), and thus can differentiate between real and fake media. Consequently, we introduce FACTOR, a practical recipe for deepfake fact checking and demonstrate its power in critical attack settings: face swapping and audio-visual synthesis. Although it is training-free, relies exclusively on off-the-shelf features, is very easy to implement, and does not see any deepfakes, it achieves better than state-of-the-art accuracy.