In this paper, we consider a single machine on-line scheduling problem with the special chains precedence and delivery time. All jobs arrive over time. The chains chainsi arrive at time ri , it is known that the processing and delivery time of each job on the chain satisfy one special condition CD a forehand: if the job J(i)j is the predecessor of the job J(i)k on the chain chaini, then they satisfy p(i)j = p(i)k = p ≥ qj ≥ qk , i = 1,2, ---,n , where pj and qj denote the processing time and the delivery time of the job Jj respectively. Obviously, if the arrival jobs have no chains precedence, it shows that the length of the corresponding chain is 1. The objective is to minimize the time by which all jobs have been delivered. We provide an on-line algorithm with a competitive ratio of √2 , and the result is the best possible.