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Previous work on pun generation commonly begins with a given pun word (a pair of homophones for heterographic pun generation and a polyseme for homographic pun generation) and seeks to generate an appropriate pun. While this may enable efficient pun generation, we believe that a pun is most entertaining if it fits appropriately within a given context, e.g., a given situation or dialogue. In this work, we propose a new task, context-situated pun generation, where a specific context represented by a set of keywords is provided, and the task is to first identify suitable pun words that are appropriate for the context, then generate puns based on the context keywords and the identified pun words. We collect CUP (Context-sitUated Pun), containing 4.5k tuples of context words and pun pairs. Based on the new data and setup, we propose a pipeline system for context-situated pun generation, including a pun word retrieval module that identifies suitable pun words for a given context, and a generation module that generates puns from context keywords and pun words. Human evaluation shows that 69% of our top retrieved pun words can be used to generate context-situated puns, and our generation module yields successful puns 31% of the time given a plausible tuple of context words and pun pair, almost tripling the yield of a state-of-the-art pun generation model. With an end-to-end evaluation, our pipeline system with the top-1 retrieved pun pair for a given context can generate successful puns 40% of the time, better than all other modeling variations but 32% lower than the human success rate. This highlights the difficulty of the task, and encourages more research in this direction.