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Leveraging nanotechnology for computing opens up exciting new avenues for breakthroughs. For example, graphene is an emerging nanoscale material and is believed to be a potential candidate for post-Si nanoelectronics due to high carrier mobility and extreme scalability. Recently, a new graphene nanoribbon crossbar (xGNR) device was proposed which exhibits negative differential resistance (NDR). In this paper we propose a novel graphene nanoribbon tunneling ternary content addressable memory (GNTCAM) enabled by xGNR device, featuring heterogeneous integration with CMOS transistors and routing. Benchmarking with respect to 16nm CMOS TCAM (which uses two binary SRAMs to store ternary information) shows that GNTCAM is up to 1.82x denser, up to 9.42x more power-efficient during stand-by, and has up to 1.6x faster performance during match operation. Thus, GNTCAM has the potential to realize low-power high-density nanoscale TCAMs. Further improvements may be possible by using graphene more extensively, as graphene transistors become available in future.