Manufacturing process variation in sub-20nm processes has introduced ever increasing overhead in Static Timing Analysis (STA) in order to guarantee the reliable operation of the circuit. Chip designers apply corner-based analysis and add guard-bands to design parameters in order to take into account the impact of process variation on timing. However, the aforementioned techniques are either too slow as the number of design parameters proliferates with the integration of more components into a chip or inaccurate due to the assumption that the worst case delay resides at the corners of design parameters. In this paper, we present a novel statistical methodology, which relies on Extreme Value Theory (EVT), to estimate the worst case delay of VLSI circuits under variations in gate/interconnect parameters. Despite the previous statistical approaches toward maximum delay estimation, our methodology can be applied regardless of the underlying gate/interconnect delay model or any assumption about the distribution of the Arrival Time (AT) at every circuit node, making it very appealing for integration to any level of timing analysis abstraction (from spice-to-gate level) and provide fast yet accurate results. Experimental results on ISCAS85/ISCAS89 circuits show that the estimated maximum AT at the Primary Outputs (POs) can be within 5% of the true maximum AT, at the cost of a few thousand Monte Carlo simulations.