Meeting the exponential increase in the global demand for bandwidth has become a major concern for today's data centers. The scalability of any data center is defined by the maximum capacity and port count of the switching devices it employs, limited by total pin bandwidth on current electronic switch ASICs. Optical switches can provide higher capacity and port counts, and hence, can be used to transform data center scalability. We have recently demonstrated a 1000-port starcoupler based wavelength division multiplexed (WDM) and time division multiplexed (TDM) optical switch architecture offering a bandwidth of 32 Tbit/s with the use of fast wavelength-tunable transmitters and high-sensitivity coherent receivers. However, the major challenge in deploying such an optical switch to replace current electronic switches lies in designing and implementing a scalable scheduler capable of operating on packet timescales. In this paper, we present a pipelined and highly parallel electronic scheduler that configures the high-radix (1000-port) optical packet switch. The scheduler can process requests from 1000 nodes and allocate timeslots across 320 wavelength channels and 4000 wavelength-tunable transceivers within a time constraint of 1µs. Using the Opencell NanGate 45nm standard cell library, we show that the complete 1000-port parallel scheduler algorithm occupies a circuit area of 52.7mm 2 , 4-8x smaller than that of a high-performance switch ASIC, with a clock period of less than 8ns, enabling 138 scheduling iterations to be performed in 1µs. The performance of the scheduling algorithm is evaluated in comparison to maximal matching from graph theory and conventional software-based wavelength allocation heuristics. The parallel hardware scheduler is shown to achieve similar matching performance and network throughput while being orders of magnitude faster.