Physically unclonable functions are used for IP protection, hardware authentication and supply chain security. While many PUF constructions have been put forward in the past decade, only few of them are applicable to FPGA platforms. Strict constraints on the placement and routing are the main disadvantages of the existing PUFs on FPGAs, because they place a high effort on the designer. In this paper we propose a new delay-based PUF construction called Monte Carlo PUF, that does not require low-level placement and routing control. This construction relies on the on-chip Monte Carlo method that is applied for measuring the delays of logic elements in order to extract a unique device fingerprint. The proposed construction allows a trade-off between the evaluation time and the error rate. The Monte Carlo PUF is implemented and evaluated on Xilinx Spartan-6 FPGAs.