Applications of true random number generators (TRNGs) span from art to numerical computing and system security. In cryptographic applications, TRNGs are used for generating new keys, nonces and masks. For this reason, a TRNG is an essential building block and often a point of failure for embedded security systems. One type of primitives that are widely used as source of randomness are ring oscillators. For a ring-oscillator-based TRNG, the true randomness originates from its timing jitter. Therefore, determining the jitter strength is essential to estimate the quality of a TRNG. In this paper, we propose a method to measure the jitter strength of a ring oscillator implemented on an FPGA. The fast tapped delay chain is utilized to perform the on-chip measurement with a high resolution. The proposed method is implemented on both a Xilinx FPGA and an Intel FPGA. Fast carry logic components on different FPGAs are used to implement the fast delay line. This carry logic component is designed to be fast and has dedicated routing, which enables a precise measurement. The differential structure of the delay chain is used to thwart the influence of undesirable noise from the measurement. The proposed methodology can be applied to other FPGA families and ASIC designs.