Given news articles about an entity, such as a public figure or organization, timeline summarization (TLS) involves generating a timeline that summarizes the key events about the entity. However, the TLS task is too underspecified, since what is of interest to each reader may vary, and hence there is not a single ideal or optimal timeline. In this paper, we introduce a novel task, called Constrained Timeline Summarization (CTLS), where a timeline is generated in which all events in the timeline meet some constraint. An example of a constrained timeline concerns the legal battles of Tiger Woods, where only events related to his legal problems are selected to appear in the timeline. We collected a new human-verified dataset of constrained timelines involving 47 entities and 5 constraints per entity. We propose an approach that employs a large language model (LLM) to summarize news articles according to a specified constraint and cluster them to identify key events to include in a constrained timeline. In addition, we propose a novel self-reflection method during summary generation, demonstrating that this approach successfully leads to improved performance.