Linear frequency modulated (LFM) radar systems are simple and easy to implement, making them ideal for inexpensive undergraduate research projects. Unfortunately, LFM radar schemes have multiple limitations that make them unviable in many real-world applications. Given the limitations of LFM radar systems, we propose a chaos-based frequency modulated (CBFM) system. In this presentation, we present the theory, design, and experimental verification of a CBFM radar system that has both ranging and synthetic aperture radar imaging capabilities. The performance of our CBFM system is compared to that of the LFM system designed by MIT. We discuss many challenges and unforeseen obstacles that were encountered while developing one of the first CBFM radar systems. Although our initial results look promising, particularly for ranging, there remains a significant amount of research and development to be done on the SAR imaging signal processing software algorithms before a CBFM radar scheme is fully functional.