A high-resolution radar ranging scheme is proposed and demonstrated based on the ultra-wideband chaotic optoelectronic oscillator (OEO). Through biasing the electro-optic intensity modulator near its minimum transmission point, high-dimensional chaotic signals with flat spectra and low time-delayed signatures can be generated in the OEO, which are favorable for increasing the ranging resolution and the confidentiality. In the experiment, the optimized broadband OEO generates a high-dimensional chaotic signal with a flat spectrum in the frequency range of 2 GHz to 16 GHz and a high permutation entropy of 0.9754. This chaotic signal is used to achieve multiple target ranging, where a ranging resolution of 1.4 cm is realized.