Novel random number generation methods and random number generators (RNG)s based on continuous-time chaotic oscillators are presented. Offset and frequency compensation loops are added to maximize the statistical quality of the output sequence and to be robust against parameter variations and attacks. We have verified both numerically and experimentally that, when the one-dimensional section was divided into regions according to distribution, the generated bit streams passed the tests used in both the FIPS-140-2 and the NIST 800-22 statistical test suites without post processing. Numerical and experimental results presented in this innovation not only verify the feasibility of the proposed circuits, but also encourage their use as the core of a high-performance IC RNG as well. In comparison with RNGs based on discrete-time chaotic maps, amplification of a noise source and jittered oscillator sampling, it is seen that RNGs based on continuous-time chaotic oscillators can offer much higher and constant data rates without post-processing. In conclusion, we can deduce that the proposed circuits can be realized in integrated circuits and the use of continuous-time chaos with the proposed innovations is very promising in generating random numbers with very high throughput.