With the exponential growth of data in various applications, sublinear algorithms have become a new paradigm in computing for solving problems involving large amount datasets. In this paper, we study the classical parallel machine scheduling problem subject to chain precedence constraints where the processing times of jobs differ no more than a constant factor c. The objective is to minimize makespan. We develop the first streaming approximation algorithm when the number of chains is sublinear to the number of jobs. And for arbitrary number or chains, we develop the first randomized approximation scheme that runs in sublinear time.