General purpose graphics processing units (GP-GPU), owing to their enormous thread-level parallelism, can significantly improve the power consumption at the near-threshold (NTC) operating region, while offering close to a super-threshold performance. However, process variation (PV) can drastically reduce the GPU performance at NTC. In this work, choke points—a unique device-level characteristic of PV at NTC—that can exacerbate the warp criticality problem in GPUs have been explored. It is shown that the modern warp schedulers cannot tackle the choke point induced critical warps in an NTC GPU. Additionally, Choke Point Aware Warp Speculator, a circuit-architectural solution is proposed to dynamically predict the critical warps in GPUs, and accelerate them in their respective execution units. The best scheme achieves an average improvement of ∼39% in performance, and ∼31% in energy-efficiency, over one state-of-the-art warp scheduler, across 15 GPGPU applications, while incurring marginal hardware overheads.