Curl was a postdoctoral fellow at Harvard University with E. B. Wilson, where he used microwave spectroscopy to study the bond rotation barriers of molecules.  After that, he joined the faculty of Rice University in 1958. He inherited the equipment and graduate students of George Bird, a professor who was leaving for a job at Polaroid.  Curl's early research involved the microwave spectroscopy of chlorine dioxide.  His research program included both experiment and theory, mainly focused on detection and analysis of free radicals using microwave spectroscopy and tunable lasers.  He used these observations to develop the theory of their fine structure and hyperfine structure, as well as information about their structure and the kinetics of their reactions.