The unprecedented use of social media through smartphones and other web-enabled mobile devices has enabled the rapid adoption of platforms like Twitter. Event detection has found many applications on the web, including breaking news identification and summarization. The recent increase in the usage of Twitter during crises has attracted researchers to focus on detecting events in tweets. However, current solutions have focused on static Twitter data. The necessity to detect events in a streaming environment during fast paced events such as a crisis presents new opportunities and challenges. In this paper, we investigate event detection in the context of real-time Twitter streams as observed in real-world crises. We highlight the key challenges in this problem: the informal nature of text, and the high-volume and high-velocity characteristics of Twitter streams. We present a novel approach to address these challenges using single-pass clustering and the compression distance to efficiently detect events in Twitter streams. Through experiments on large Twitter datasets, we demonstrate that the proposed framework is able to detect events in near real-time and can scale to large and noisy Twitter streams.