We propose Greedy Topology-Aware Quantum Circuit Partitioning (GTQCP), a novel quantum gate circuit partitioning method which partitions circuits by applying a greedy heuristic to the qubit dependency graph of the circuit. GTQCP is compared against three other gate partitioning methods, two of which (QuickPartitioner and ScanPartitioner) are part of the Berkley Quantum Synthesis Toolkit. GTQCP is shown to have 18% run time improvement ratio over the fastest approach (QuickPartitioner), and a 96% improvement over the highest quality approach (ScanPartitioner). The algorithm also demonstrates nearly identical result quality (number of partitions) compared with ScanPartitioner, and a 38% quality improvement over QuickPartitioner.