A private machine learning algorithm hides as much as possible about its training data while still preserving accuracy. In this work, we study whether a non-private learning algorithm can be made private by relying on an instance-encoding mechanism that modifies the training inputs before feeding them to a normal learner. We formalize both the notion of instance encoding and its privacy by providing two attack models. We first prove impossibility results for achieving a (stronger) model. Next, we demonstrate practical attacks in the second (weaker) attack model on InstaHide, a recent proposal by Huang, Song, Li and Arora [ICML'20] that aims to use instance encoding for privacy.