Language models have been shown to perform better with an increase in scale on a wide variety of tasks via the in-context learning paradigm. In this paper, we investigate the hypothesis that the ability of a large language model to in-context learn-perform a task is not uniformly spread across all of its underlying components. Using a 66 billion parameter language model (OPT-66B) across a diverse set of 14 downstream tasks, we find this is indeed the case: ~70\% of the attention heads and ~20\% of the feed forward networks can be removed with minimal decline in task performance. We find substantial overlap in the set of attention heads (un)important for in-context learning across tasks and number of in-context examples. We also address our hypothesis through a task-agnostic lens, finding that a small set of attention heads in OPT-66B score highly on their ability to perform primitive induction operations associated with in-context learning, namely, prefix matching and copying. These induction heads overlap with task-specific important heads, reinforcing arguments by Olsson et al. (2022) regarding induction head generality to more sophisticated behaviors associated with in-context learning. Overall, our study provides several insights that indicate large language models may be under-trained for in-context learning and opens up questions on how to pre-train language models to more effectively perform in-context learning.