This paper introduces a VLSI (Very Large Scale Integrated Circuit) implementation of the 2-D Discrete Cosine Transform (DCT) with an application to image and video coding. This implementation, which is based upon a state space model, uses both algorithm and data partitioning to achieve high efficiency. With this implementation, the amount of data transfers between the processing elements (PEs) are reduced and all the data transfers are limitted to be local. This system accepts the input as a progressively scanned data stream which reduces the hardware required for the input data control module. With proper ordering of computations, a matrix transposition between two matrix by matrix multiplications, which is required in many 2-D DCT systems based upon a row-column decomposition, can be also removed. The new implementation scheme makes it feasible to implement a single 2-D DCT VLSI chip which can be easily expanded for a larger 2-D DCT by cascading these chips.