It has been suggested that chat system provides real time communication like direct conversation. However, chat conversation has distinctive complexity compared with direct and telephone conversation. One often has difficulty in determining whether he is the <i>talker</i> or the <i>watcher</i>. Furthermore, it is not always clear for one that which topic appearing on the record should be referred to. In the present paper, the authors investigated how the order in chat conversation is established, and what kind of efforts are made by the participants. Generally speaking, the couples of subjects maintained the order by sending messages alternately, suggesting that they could basically determine whether they were the <i>talker</i> or the <i>watcher</i>. However, the order was easily broken down when one sent a message so as to interrupt the other's sending. It is discussed that one of the reasons that such interrupting messages were sent was duality of the meaning of an interval between two successive messages; the interval might simultaneously be a sign of the other participant's <i>silence</i> and that of the other's taking time to prepare his/her message. Breaking down of the order were often followed by the situation that several threads appeared on the display were maintained for a while, implying that order with more complicated interaction could emerge through the failure at taking the roles of <i>talker</i> and <i>watcher</i> alternately.