High entropy waveforms exhibit desirable correlation properties in radar and sonar applications when multiple systems are used in close proximity. Unfortunately, the information content of these signals can impose high sampling requirements for digital detection techniques. Solvable chaotic oscillators have been proposed to address such issues due to their simple, matched filters, where hardware has been demonstrated with a bandwidth of 10-20 kHz. To extend applications of these systems, we present theory, design, and experimental verification of solvable chaos at 1 MHz using simple off-the-shelf components. The waveforms produced by this system were propagated over a 2.45 GHz RF link and detected with an RLC-based, purely analog matched filter. Further, we show that properties of this special class of chaotic systems can be exploited to yield RF noise sources that are generally advantageous for multi-user ranging applications when compared to conventional techniques. The result is a simple, low-cost, and potentially low-power RF ranging system that requires very little digital signal processing.