Social networks have been instrumental in spreading rumor such as fake news and false rumors. Research in rumor intervention to date has concentrated on launching an intervening campaign to limit the number of infectees. However, many emerging and important tasks focus more onearly intervention. Social and psychological studies have revealed that rumors might evolve 70% of its original content after 6 transmissions. Therefore, ignoring earliness of intervention makes the intervening campaign downgrade rapidly due to the evolved content. In real social networks, the number of social actors is usuallylarge, while the budget for an intervening campaign is relativelysmall. The limited budget makes early intervention particularly challenging. Nonetheless, we present an efficient containment method that promptly terminates the diffusion with least cost. To our knowledge, this work is the first to study the earliness of rumor intervention in a large real-world social network. Evaluations on a network of $3$ million users show that the key social actors who earliest terminate the spread are not necessarily the most influential users or friends of rumor initiators, and the proposed method effectively reduces the life span of rumors.