Because state-of-the-art language models are expensive to train, most practitioners must make use of one of the few publicly available language models or language model APIs. This consolidation of trust increases the potency of backdoor attacks, where an adversary tampers with a machine learning model in order to make it perform some malicious behavior on inputs that contain a predefined backdoor trigger. We show that the in-context learning ability of large language models significantly complicates the question of developing backdoor attacks, as a successful backdoor must work against various prompting strategies and should not affect the model's general purpose capabilities. We design a new attack for eliciting targeted misclassification when language models are prompted to perform a particular target task and demonstrate the feasibility of this attack by backdooring multiple large language models ranging in size from 1.3 billion to 6 billion parameters. Finally we study defenses to mitigate the potential harms of our attack: for example, while in the white-box setting we show that fine-tuning models for as few as 500 steps suffices to remove the backdoor behavior, in the black-box setting we are unable to develop a successful defense that relies on prompt engineering alone.