Schaeffer (1997, 2000) argues that children lack knowledge of specificity because Dutch children omit determiners and fail to scramble pronouns. Avrutin & Brun (2001), however, find that Russian children place arguments correctly according to whether they are specific or non-specific. This paper investigates object agreement and specificity in early Swahili. Object agreement in Swahili is obligatory when the object is specific, but is prohibited when the object is non-specific. Analysis of naturalistic data from four Swahili-speaking children (1;8-3;2) reveals that children overwhelmingly provide object agreement in obligatory contexts (when the object is a personal name, is topicalized, or refers to first/second person). The supply of object agreement cannot be due to a general strategy of overusing agreement, since object agreement does not occur in prohibited contexts such as intransitive clauses. I conclude that object agreement and knowledge of specificity are acquired by Swahili children before the age of two years. (Contains 1 footnote.)