The conventional synchronous design approach is not suitable for implementing self-timed circuits on FPGAs. When design tools try to meet synchronous circuits timing constraints, they can violate self-timed setup timing constraints. This paper proposes a new methodology for implementing self-timed circuits in modern FPGAs using the Xilinx Hierarchical Design flow and a convenient architecture of a configurable delay element. Reported simulation results, in accordance with static timing analysis, show that the self-timed timing constraints are satisfied using our design methodology.